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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 867.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
867.c1 | 867a2 | \([0, -1, 1, -17147, -859018]\) | \(-23100424192/14739\) | \(-355763629491\) | \([]\) | \(1728\) | \(1.1574\) | |
867.c2 | 867a1 | \([0, -1, 1, 193, -5023]\) | \(32768/459\) | \(-11079144171\) | \([]\) | \(576\) | \(0.60808\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 867.c have rank \(1\).
Complex multiplication
The elliptic curves in class 867.c do not have complex multiplication.Modular form 867.2.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.