Properties

Label 75712.ce
Number of curves $1$
Conductor $75712$
CM no
Rank $1$

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Show commands: SageMath
sage: E = EllipticCurve("ce1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 75712.ce

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
75712.ce1 75712co1 \([0, 1, 0, -38081, 9008351]\) \(-1352/7\) \(-31621429426356224\) \([]\) \(419328\) \(1.8503\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 75712.ce1 has rank \(1\).

Complex multiplication

The elliptic curves in class 75712.ce do not have complex multiplication.

Modular form 75712.2.a.ce

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + q^{7} - 2q^{9} - 4q^{11} - q^{15} - 6q^{17} - 4q^{19} + O(q^{20})\)  Toggle raw display