Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("z1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 75712.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
75712.z1 75712ct1 \([0, -1, 0, -225, -4031]\) \(-1352/7\) \(-6551207936\) \([]\) \(32256\) \(0.56784\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 75712.z1 has rank \(1\).

Complex multiplication

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

Modular form 75712.2.a.z

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