Properties

Label 75712r
Number of curves $1$
Conductor $75712$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 75712r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
75712.c1 75712r1 \([0, 0, 0, -239980, 988157872]\) \(-1207949625/332678528\) \(-420944468523654053888\) \([]\) \(4515840\) \(2.6366\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 75712r1 has rank \(1\).

Complex multiplication

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

Modular form 75712.2.a.r

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