Properties

Label 5415.j
Number of curves $8$
Conductor $5415$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5415.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5415.j1 5415k7 \([1, 0, 1, -779768, 264965501]\) \(1114544804970241/405\) \(19053581805\) \([2]\) \(27648\) \(1.7631\)  
5415.j2 5415k5 \([1, 0, 1, -48743, 4135781]\) \(272223782641/164025\) \(7716700631025\) \([2, 2]\) \(13824\) \(1.4165\)  
5415.j3 5415k8 \([1, 0, 1, -39718, 5716961]\) \(-147281603041/215233605\) \(-10125854568031005\) \([2]\) \(27648\) \(1.7631\)  
5415.j4 5415k3 \([1, 0, 1, -28888, -1892197]\) \(56667352321/15\) \(705688215\) \([2]\) \(6912\) \(1.0699\)  
5415.j5 5415k4 \([1, 0, 1, -3618, 38431]\) \(111284641/50625\) \(2381697725625\) \([2, 2]\) \(6912\) \(1.0699\)  
5415.j6 5415k2 \([1, 0, 1, -1813, -29437]\) \(13997521/225\) \(10585323225\) \([2, 2]\) \(3456\) \(0.72337\)  
5415.j7 5415k1 \([1, 0, 1, -8, -1279]\) \(-1/15\) \(-705688215\) \([2]\) \(1728\) \(0.37679\) \(\Gamma_0(N)\)-optimal
5415.j8 5415k6 \([1, 0, 1, 12627, 291853]\) \(4733169839/3515625\) \(-165395675390625\) \([2]\) \(13824\) \(1.4165\)  

Rank

sage: E.rank()
 

The elliptic curves in class 5415.j have rank \(0\).

Complex multiplication

The elliptic curves in class 5415.j do not have complex multiplication.

Modular form 5415.2.a.j

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} - q^{4} + q^{5} + q^{6} - 3q^{8} + q^{9} + q^{10} - 4q^{11} - q^{12} + 2q^{13} + q^{15} - q^{16} + 2q^{17} + q^{18} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 16 & 4 & 8 & 16 & 8 \\ 2 & 1 & 2 & 8 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 16 & 4 & 8 & 16 & 8 \\ 16 & 8 & 16 & 1 & 4 & 2 & 4 & 8 \\ 4 & 2 & 4 & 4 & 1 & 2 & 4 & 2 \\ 8 & 4 & 8 & 2 & 2 & 1 & 2 & 4 \\ 16 & 8 & 16 & 4 & 4 & 2 & 1 & 8 \\ 8 & 4 & 8 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.