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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 78400.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
78400.r1 | 78400dh1 | \([0, 0, 0, -700, 7000]\) | \(48384\) | \(784000000\) | \([]\) | \(53760\) | \(0.49693\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 78400.r1 has rank \(0\).
Complex multiplication
The elliptic curves in class 78400.r do not have complex multiplication.Modular form 78400.2.a.r
sage: E.q_eigenform(10)