Properties

Label 363726.f
Number of curves $1$
Conductor $363726$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 363726.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
363726.f1 363726f1 \([1, -1, 0, -219456, 39617716]\) \(905072904217/198396\) \(256222079177724\) \([]\) \(2211840\) \(1.7586\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 363726.f1 has rank \(2\).

Complex multiplication

The elliptic curves in class 363726.f do not have complex multiplication.

Modular form 363726.2.a.f

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - 3 q^{5} + q^{7} - q^{8} + 3 q^{10} + q^{13} - q^{14} + q^{16} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display