Properties

Label 88445.z
Number of curves $1$
Conductor $88445$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("z1")
 
E.isogeny_class()
 

Elliptic curves in class 88445.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
88445.z1 88445bi1 \([1, -1, 0, -61504, -5862347]\) \(-92959677/125\) \(-34598173801625\) \([]\) \(698880\) \(1.5036\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 88445.z1 has rank \(1\).

Complex multiplication

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

Modular form 88445.2.a.z

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