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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 507.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
507.c1 | 507a2 | \([1, 1, 0, -12678, -3060351]\) | \(-276301129/4782969\) | \(-3901614750890649\) | \([]\) | \(2184\) | \(1.6728\) | |
507.c2 | 507a1 | \([1, 1, 0, -1693, 26434]\) | \(-658489/9\) | \(-7341576489\) | \([]\) | \(312\) | \(0.69989\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 507.c have rank \(1\).
Complex multiplication
The elliptic curves in class 507.c do not have complex multiplication.Modular form 507.2.a.c
sage: E.q_eigenform(10)
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.