Properties

Label 29575s
Number of curves $1$
Conductor $29575$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 29575s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
29575.b1 29575s1 \([0, -1, 1, -35208, 1931568]\) \(2560000/637\) \(1201045833203125\) \([]\) \(161280\) \(1.6037\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 29575s1 has rank \(2\).

Complex multiplication

The elliptic curves in class 29575s do not have complex multiplication.

Modular form 29575.2.a.s

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