Properties

Label 975.e
Number of curves $1$
Conductor $975$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 975.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
975.e1 975k1 \([1, 0, 0, 12, 117]\) \(304175/9477\) \(-5923125\) \([]\) \(144\) \(-0.020457\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 975.e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 975.e do not have complex multiplication.

Modular form 975.2.a.e

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