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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 4950c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4950.m1 | 4950c1 | \([1, -1, 0, -3417, -70759]\) | \(14348907/1100\) | \(338301562500\) | \([2]\) | \(4608\) | \(0.95695\) | \(\Gamma_0(N)\)-optimal |
4950.m2 | 4950c2 | \([1, -1, 0, 3333, -320509]\) | \(13312053/151250\) | \(-46516464843750\) | \([2]\) | \(9216\) | \(1.3035\) |
Rank
sage: E.rank()
The elliptic curves in class 4950c have rank \(0\).
Complex multiplication
The elliptic curves in class 4950c do not have complex multiplication.Modular form 4950.2.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 Cremona 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 Cremona labels.