Label 413712.i
Number of curves $1$
Conductor $413712$
CM no
Rank $1$

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Show commands for: SageMath
sage: E = EllipticCurve("i1")
sage: E.isogeny_class()

Elliptic curves in class 413712.i

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
413712.i1 413712i1 \([0, 0, 0, -8112, -500240]\) \(-692224/867\) \(-73940091383808\) \([]\) \(1674240\) \(1.3546\) \(\Gamma_0(N)\)-optimal


sage: E.rank()

The elliptic curve 413712.i1 has rank \(1\).

Complex multiplication

The elliptic curves in class 413712.i do not have complex multiplication.

Modular form 413712.2.a.i

sage: E.q_eigenform(10)
\(q - 4q^{5} + 3q^{7} + 4q^{11} - q^{17} + 4q^{19} + O(q^{20})\)  Toggle raw display