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Properties

Label 2310.h
Number of curves $8$
Conductor $2310$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 2310.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2310.h1 2310g7 \([1, 0, 1, -25467989, -49471735264]\) \(1826870018430810435423307849/7641104625000000000\) \(7641104625000000000\) \([2]\) \(165888\) \(2.8322\)  
2310.h2 2310g6 \([1, 0, 1, -1616469, -747850208]\) \(467116778179943012100169/28800309694464000000\) \(28800309694464000000\) \([2, 2]\) \(82944\) \(2.4857\)  
2310.h3 2310g4 \([1, 0, 1, -437774, -9825928]\) \(9278380528613437145689/5328033205714065000\) \(5328033205714065000\) \([6]\) \(55296\) \(2.2829\)  
2310.h4 2310g3 \([1, 0, 1, -305749, 50640416]\) \(3160944030998056790089/720291785342976000\) \(720291785342976000\) \([2]\) \(41472\) \(2.1391\)  
2310.h5 2310g2 \([1, 0, 1, -286854, 58872856]\) \(2610383204210122997209/12104550027662400\) \(12104550027662400\) \([2, 6]\) \(27648\) \(1.9364\)  
2310.h6 2310g1 \([1, 0, 1, -286534, 59011352]\) \(2601656892010848045529/56330588160\) \(56330588160\) \([6]\) \(13824\) \(1.5898\) \(\Gamma_0(N)\)-optimal
2310.h7 2310g5 \([1, 0, 1, -141054, 118709176]\) \(-310366976336070130009/5909282337130963560\) \(-5909282337130963560\) \([6]\) \(55296\) \(2.2829\)  
2310.h8 2310g8 \([1, 0, 1, 1263531, -3122122208]\) \(223090928422700449019831/4340371122724101696000\) \(-4340371122724101696000\) \([2]\) \(165888\) \(2.8322\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2310.h have rank \(1\).

Complex multiplication

The elliptic curves in class 2310.h do not have complex multiplication.

Modular form 2310.2.a.h

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} + q^{7} - q^{8} + q^{9} + q^{10} - q^{11} + q^{12} + 2 q^{13} - q^{14} - q^{15} + q^{16} - 6 q^{17} - q^{18} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.