Properties

Label 75118.i
Number of curves $1$
Conductor $75118$
CM no
Rank $1$

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

Elliptic curves in class 75118.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
75118.i1 75118h1 \([1, -1, 0, -1389253, -627317419]\) \(2003092024307193/9529458688\) \(1410701888566853632\) \([]\) \(3927528\) \(2.3318\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 75118.i1 has rank \(1\).

Complex multiplication

The elliptic curves in class 75118.i do not have complex multiplication.

Modular form 75118.2.a.i

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