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SageMath
E = EllipticCurve("cr1")
E.isogeny_class()
Elliptic curves in class 121968.cr
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
121968.cr1 | 121968r1 | \([0, 0, 0, -363, -11979]\) | \(-6912/77\) | \(-58929205104\) | \([]\) | \(61440\) | \(0.74864\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 121968.cr1 has rank \(1\).
Complex multiplication
The elliptic curves in class 121968.cr do not have complex multiplication.Modular form 121968.2.a.cr
sage: E.q_eigenform(10)