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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 18515.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
18515.r1 | 18515f1 | \([0, 0, 1, -1421423, -649419841]\) | \(1134964776505135104/5744580078125\) | \(1607569033642578125\) | \([]\) | \(513216\) | \(2.3400\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 18515.r1 has rank \(0\).
Complex multiplication
The elliptic curves in class 18515.r do not have complex multiplication.Modular form 18515.2.a.r
sage: E.q_eigenform(10)