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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 1936.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1936.c1 | 1936h2 | \([0, -1, 0, -9357, -347279]\) | \(-199794688/1331\) | \(-603634608896\) | \([]\) | \(2880\) | \(1.0960\) | |
1936.c2 | 1936h1 | \([0, -1, 0, 323, -2671]\) | \(8192/11\) | \(-4988715776\) | \([]\) | \(960\) | \(0.54665\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1936.c have rank \(1\).
Complex multiplication
The elliptic curves in class 1936.c do not have complex multiplication.Modular form 1936.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.