Properties

Label 5415.l
Number of curves $1$
Conductor $5415$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 5415.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5415.l1 5415i1 \([0, 1, 1, -4734996, -2692708189]\) \(1914902401024/597871125\) \(3665587481001023896125\) \([]\) \(402192\) \(2.8421\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 5415.l1 has rank \(1\).

Complex multiplication

The elliptic curves in class 5415.l do not have complex multiplication.

Modular form 5415.2.a.l

sage: E.q_eigenform(10)
 
\(q + 2 q^{2} + q^{3} + 2 q^{4} - q^{5} + 2 q^{6} - 2 q^{7} + q^{9} - 2 q^{10} + q^{11} + 2 q^{12} - 2 q^{13} - 4 q^{14} - q^{15} - 4 q^{16} + 2 q^{17} + 2 q^{18} + O(q^{20})\) Copy content Toggle raw display