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SageMath
E = EllipticCurve("dp1")
E.isogeny_class()
Elliptic curves in class 19600.dp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
19600.dp1 | 19600s1 | \([0, -1, 0, -6008, 210512]\) | \(-15298178/3125\) | \(-4900000000000\) | \([]\) | \(34560\) | \(1.1573\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 19600.dp1 has rank \(0\).
Complex multiplication
The elliptic curves in class 19600.dp do not have complex multiplication.Modular form 19600.2.a.dp
sage: E.q_eigenform(10)