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Properties

Label 372810.a
Number of curves $2$
Conductor $372810$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 372810.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
372810.a1 372810a2 \([1, 1, 0, -7953, -246297]\) \(2305199161/277350\) \(6694554762150\) \([2]\) \(1161216\) \(1.1918\)  
372810.a2 372810a1 \([1, 1, 0, 717, -19143]\) \(1685159/7740\) \(-186824784060\) \([2]\) \(580608\) \(0.84519\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 372810.a have rank \(0\).

Complex multiplication

The elliptic curves in class 372810.a do not have complex multiplication.

Modular form 372810.2.a.a

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.