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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 4114c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4114.c1 | 4114c1 | \([1, -1, 1, -3895, 11663]\) | \(3687953625/2106368\) | \(3731559400448\) | \([2]\) | \(4800\) | \(1.1021\) | \(\Gamma_0(N)\)-optimal |
4114.c2 | 4114c2 | \([1, -1, 1, 15465, 81359]\) | \(230910510375/135399968\) | \(-239869302710048\) | \([2]\) | \(9600\) | \(1.4487\) |
Rank
sage: E.rank()
The elliptic curves in class 4114c have rank \(0\).
Complex multiplication
The elliptic curves in class 4114c do not have complex multiplication.Modular form 4114.2.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.