Properties

Label 69575.c
Number of curves $1$
Conductor $69575$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 69575.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
69575.c1 69575z1 \([0, -1, 1, -55458, -5026682]\) \(-5451776/23\) \(-79581841796875\) \([]\) \(403200\) \(1.5220\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 69575.c1 has rank \(1\).

Complex multiplication

The elliptic curves in class 69575.c do not have complex multiplication.

Modular form 69575.2.a.c

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