Properties

Label 37570.i
Number of curves $1$
Conductor $37570$
CM no
Rank $1$

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

Elliptic curves in class 37570.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
37570.i1 37570n1 \([1, 1, 1, -1145, 14487]\) \(-574468255729/2284880\) \(-660330320\) \([]\) \(19584\) \(0.54952\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 37570.i1 has rank \(1\).

Complex multiplication

The elliptic curves in class 37570.i do not have complex multiplication.

Modular form 37570.2.a.i

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + 3 q^{7} + q^{8} - 2 q^{9} + q^{10} - 2 q^{11} - q^{12} - q^{13} + 3 q^{14} - q^{15} + q^{16} - 2 q^{18} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display