Properties

Label 270480.ig
Number of curves $8$
Conductor $270480$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ig1")
 
E.isogeny_class()
 

Elliptic curves in class 270480.ig

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
270480.ig1 270480ig7 \([0, 1, 0, -199056828560, -32072636951597292]\) \(1810117493172631097464564372609/125368453502655029296875000\) \(60413842170404296875000000000000000\) \([2]\) \(2293235712\) \(5.4218\)  
270480.ig2 270480ig6 \([0, 1, 0, -195622814480, -33302452172433900]\) \(1718043013877225552292911401729/9180538178765625000000\) \(4424012333848973376000000000000\) \([2, 2]\) \(1146617856\) \(5.0753\)  
270480.ig3 270480ig3 \([0, 1, 0, -195622563600, -33302541862134252]\) \(1718036403880129446396978632449/49057344000000\) \(23640258413592576000000\) \([2]\) \(573308928\) \(4.7287\)  
270480.ig4 270480ig8 \([0, 1, 0, -192192814480, -34526527248433900]\) \(-1629247127728109256861881401729/125809119536174660320875000\) \(-60626194859259546059123191296000000\) \([4]\) \(2293235712\) \(5.4218\)  
270480.ig5 270480ig4 \([0, 1, 0, -37096509200, 2740652917972500]\) \(11715873038622856702991202049/46415372499833400000000\) \(22367117964217957075353600000000\) \([2]\) \(764411904\) \(4.8725\)  
270480.ig6 270480ig2 \([0, 1, 0, -3444469520, -3078642033132]\) \(9378698233516887309850369/5418996968417034240000\) \(2611362096485563028692008960000\) \([2, 2]\) \(382205952\) \(4.5260\)  
270480.ig7 270480ig1 \([0, 1, 0, -2416865040, -45612835627500]\) \(3239908336204082689644289/9880281924658790400\) \(4761212060279529602128281600\) \([2]\) \(191102976\) \(4.1794\) \(\Gamma_0(N)\)-optimal
270480.ig8 270480ig5 \([0, 1, 0, 13765898480, -24605370327532]\) \(598672364899527954087397631/346996861747253448998400\) \(-167214423194429935702887471513600\) \([4]\) \(764411904\) \(4.8725\)  

Rank

sage: E.rank()
 

The elliptic curves in class 270480.ig have rank \(0\).

Complex multiplication

The elliptic curves in class 270480.ig do not have complex multiplication.

Modular form 270480.2.a.ig

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} + q^{9} - 2 q^{13} + q^{15} - 6 q^{17} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 3 & 6 & 12 & 12 \\ 2 & 1 & 2 & 2 & 6 & 3 & 6 & 6 \\ 4 & 2 & 1 & 4 & 12 & 6 & 3 & 12 \\ 4 & 2 & 4 & 1 & 12 & 6 & 12 & 3 \\ 3 & 6 & 12 & 12 & 1 & 2 & 4 & 4 \\ 6 & 3 & 6 & 6 & 2 & 1 & 2 & 2 \\ 12 & 6 & 3 & 12 & 4 & 2 & 1 & 4 \\ 12 & 6 & 12 & 3 & 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.