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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 249090c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
249090.c2 | 249090c1 | \([1, 1, 0, -1057067933, -13229078435607]\) | \(-2776583906674595739386209/93760019539193340\) | \(-4411022721798564709632540\) | \([2]\) | \(152064000\) | \(3.8210\) | \(\Gamma_0(N)\)-optimal |
249090.c1 | 249090c2 | \([1, 1, 0, -16913224003, -846625470243593]\) | \(11373164188748320280858647489/12968007753150\) | \(610091349561772275150\) | \([2]\) | \(304128000\) | \(4.1676\) |
Rank
sage: E.rank()
The elliptic curves in class 249090c have rank \(1\).
Complex multiplication
The elliptic curves in class 249090c do not have complex multiplication.Modular form 249090.2.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.