Show commands:
SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 4815.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4815.a1 | 4815e1 | \([0, 0, 1, -22053, -138146]\) | \(1627043694800896/930267028125\) | \(678164663503125\) | \([]\) | \(24000\) | \(1.5356\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 4815.a1 has rank \(1\).
Complex multiplication
The elliptic curves in class 4815.a do not have complex multiplication.Modular form 4815.2.a.a
sage: E.q_eigenform(10)