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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 4014.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4014.c1 | 4014c2 | \([1, -1, 0, -342, 2380]\) | \(6078390625/397832\) | \(290019528\) | \([2]\) | \(1728\) | \(0.37359\) | |
4014.c2 | 4014c1 | \([1, -1, 0, 18, 148]\) | \(857375/14272\) | \(-10404288\) | \([2]\) | \(864\) | \(0.027013\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4014.c have rank \(0\).
Complex multiplication
The elliptic curves in class 4014.c do not have complex multiplication.Modular form 4014.2.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.