Properties

Label 37830.i
Number of curves $1$
Conductor $37830$
CM no
Rank $1$

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

Elliptic curves in class 37830.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
37830.i1 37830f1 \([1, 1, 0, -99418227, -381595912659]\) \(-108673026027798157289434731961/2730875291015625000000\) \(-2730875291015625000000\) \([]\) \(6151680\) \(3.2215\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 37830.i1 has rank \(1\).

Complex multiplication

The elliptic curves in class 37830.i do not have complex multiplication.

Modular form 37830.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} + q^{7} - q^{8} + q^{9} - q^{10} - 5 q^{11} - q^{12} + q^{13} - q^{14} - q^{15} + q^{16} - 5 q^{17} - q^{18} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display