Show commands:
SageMath
E = EllipticCurve("rk1")
E.isogeny_class()
Elliptic curves in class 176400rk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
176400.qf1 | 176400rk1 | \([0, 0, 0, 437325, -251504750]\) | \(68782/243\) | \(-32678950487904000000\) | \([]\) | \(3763200\) | \(2.4274\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 176400rk1 has rank \(0\).
Complex multiplication
The elliptic curves in class 176400rk do not have complex multiplication.Modular form 176400.2.a.rk
sage: E.q_eigenform(10)