Properties

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

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 372810.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
372810.c1 372810c2 \([1, 1, 0, -344577298, 2461691961652]\) \(920951868692595924370239353/46802812500000000000\) \(229942217812500000000000\) \([2]\) \(90832896\) \(3.5528\)  
372810.c2 372810c1 \([1, 1, 0, -22703378, 34054482228]\) \(263419801326311610134393/50412272025600000000\) \(247675492461772800000000\) \([2]\) \(45416448\) \(3.2062\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 372810.2.a.c

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