Properties

Label 8712.i
Number of curves $1$
Conductor $8712$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 8712.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8712.i1 8712r1 \([0, 0, 0, 132, 484]\) \(1024\) \(-248396544\) \([]\) \(2880\) \(0.29790\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 8712.i1 has rank \(1\).

Complex multiplication

The elliptic curves in class 8712.i do not have complex multiplication.

Modular form 8712.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{5} - 4 q^{7} - 4 q^{13} + 4 q^{17} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display