Properties

Label 5712r
Number of curves $1$
Conductor $5712$
CM no
Rank $0$

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

Elliptic curves in class 5712r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5712.u1 5712r1 \([0, 1, 0, -85, 1091]\) \(-16777216/122451\) \(-501559296\) \([]\) \(2304\) \(0.35253\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 5712r1 has rank \(0\).

Complex multiplication

The elliptic curves in class 5712r do not have complex multiplication.

Modular form 5712.2.a.r

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} - q^{7} + q^{9} + 5 q^{11} - 5 q^{13} + q^{15} + q^{17} + 5 q^{19} + O(q^{20})\) Copy content Toggle raw display