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Properties

Label 2415.b
Number of curves $4$
Conductor $2415$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 2415.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2415.b1 2415f3 \([1, 0, 0, -46001, 3793680]\) \(10765299591712341649/20708625\) \(20708625\) \([2]\) \(4224\) \(1.0855\)  
2415.b2 2415f2 \([1, 0, 0, -2876, 59055]\) \(2630872462131649/3645140625\) \(3645140625\) \([2, 2]\) \(2112\) \(0.73890\)  
2415.b3 2415f4 \([1, 0, 0, -2071, 93026]\) \(-982374577874929/3183837890625\) \(-3183837890625\) \([2]\) \(4224\) \(1.0855\)  
2415.b4 2415f1 \([1, 0, 0, -231, 336]\) \(1363569097969/734582625\) \(734582625\) \([2]\) \(1056\) \(0.39233\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2415.b have rank \(0\).

Complex multiplication

The elliptic curves in class 2415.b do not have complex multiplication.

Modular form 2415.2.a.b

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

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.