Properties

Label 637.c
Number of curves $2$
Conductor $637$
CM no
Rank $1$
Graph

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

Elliptic curves in class 637.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
637.c1 637a1 \([1, -1, 0, -107, 454]\) \(-56723625/13\) \(-31213\) \([]\) \(60\) \(-0.14604\) \(\Gamma_0(N)\)-optimal
637.c2 637a2 \([1, -1, 0, 628, -17823]\) \(11397810375/62748517\) \(-150659189317\) \([]\) \(420\) \(0.82691\)  

Rank

sage: E.rank()
 

The elliptic curves in class 637.c have rank \(1\).

Complex multiplication

The elliptic curves in class 637.c do not have complex multiplication.

Modular form 637.2.a.c

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

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.