Properties

Label 88445r
Number of curves $1$
Conductor $88445$
CM no
Rank $1$

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

Elliptic curves in class 88445r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
88445.i1 88445r1 \([1, 1, 1, -36, -92]\) \(292201/25\) \(442225\) \([]\) \(10368\) \(-0.17550\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 88445r1 has rank \(1\).

Complex multiplication

The elliptic curves in class 88445r do not have complex multiplication.

Modular form 88445.2.a.r

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} - q^{4} - q^{5} + q^{6} + 3 q^{8} - 2 q^{9} + q^{10} + 3 q^{11} + q^{12} - 7 q^{13} + q^{15} - q^{16} + 3 q^{17} + 2 q^{18} + O(q^{20})\) Copy content Toggle raw display