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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 14700.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14700.c1 | 14700v1 | \([0, -1, 0, -16333, -748838]\) | \(131072/9\) | \(33088781250000\) | \([2]\) | \(34560\) | \(1.3424\) | \(\Gamma_0(N)\)-optimal |
14700.c2 | 14700v2 | \([0, -1, 0, 14292, -3260088]\) | \(5488/81\) | \(-4764784500000000\) | \([2]\) | \(69120\) | \(1.6890\) |
Rank
sage: E.rank()
The elliptic curves in class 14700.c have rank \(0\).
Complex multiplication
The elliptic curves in class 14700.c do not have complex multiplication.Modular form 14700.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.