Show commands:
SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 78400.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
78400.m1 | 78400fs1 | \([0, 0, 0, 48020, -73950800]\) | \(1323/256\) | \(-2369574133563392000\) | \([]\) | \(1548288\) | \(2.2050\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 78400.m1 has rank \(1\).
Complex multiplication
The elliptic curves in class 78400.m do not have complex multiplication.Modular form 78400.2.a.m
sage: E.q_eigenform(10)