Properties

Label 97175.a
Number of curves $1$
Conductor $97175$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 97175.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
97175.a1 97175q1 \([0, -1, 1, -77458, 8353568]\) \(-5451776/23\) \(-216829310546875\) \([]\) \(645120\) \(1.6055\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 97175.a1 has rank \(2\).

Complex multiplication

The elliptic curves in class 97175.a do not have complex multiplication.

Modular form 97175.2.a.a

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