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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 286650.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
286650.c1 | 286650c1 | \([1, -1, 0, -1086192, -422887284]\) | \(105756712489/3478020\) | \(4660879440006562500\) | \([2]\) | \(8847360\) | \(2.3554\) | \(\Gamma_0(N)\)-optimal |
286650.c2 | 286650c2 | \([1, -1, 0, 347058, -1459127034]\) | \(3449795831/688246650\) | \(-922316335339760156250\) | \([2]\) | \(17694720\) | \(2.7020\) |
Rank
sage: E.rank()
The elliptic curves in class 286650.c have rank \(1\).
Complex multiplication
The elliptic curves in class 286650.c do not have complex multiplication.Modular form 286650.2.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.