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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 7920.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7920.s1 | 7920bm1 | \([0, 0, 0, -12747, 559226]\) | \(-76711450249/851840\) | \(-2543580610560\) | \([]\) | \(20160\) | \(1.1953\) | \(\Gamma_0(N)\)-optimal |
7920.s2 | 7920bm2 | \([0, 0, 0, 42693, 2898794]\) | \(2882081488391/2883584000\) | \(-8610335686656000\) | \([]\) | \(60480\) | \(1.7446\) |
Rank
sage: E.rank()
The elliptic curves in class 7920.s have rank \(1\).
Complex multiplication
The elliptic curves in class 7920.s do not have complex multiplication.Modular form 7920.2.a.s
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.