Properties

Label 81232c
Number of curves $1$
Conductor $81232$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 81232c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
81232.a1 81232c1 \([0, 1, 0, -109, -473]\) \(564600832/5077\) \(1299712\) \([]\) \(9600\) \(-0.0041184\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 81232c1 has rank \(2\).

Complex multiplication

The elliptic curves in class 81232c do not have complex multiplication.

Modular form 81232.2.a.c

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{5} - 2 q^{9} - 4 q^{11} - 2 q^{13} - 2 q^{15} - 6 q^{17} + q^{19} + O(q^{20})\) Copy content Toggle raw display