Properties

Label 370881.z
Number of curves $1$
Conductor $370881$
CM no
Rank $1$

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

Elliptic curves in class 370881.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
370881.z1 370881z1 \([1, -1, 0, -480688686, 3686430745003]\) \(170295687079857398473/17163597526568829\) \(1237998408279821441290381869\) \([]\) \(263577600\) \(3.9347\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 370881.z1 has rank \(1\).

Complex multiplication

The elliptic curves in class 370881.z do not have complex multiplication.

Modular form 370881.2.a.z

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} - 3 q^{5} - 3 q^{8} - 3 q^{10} - 6 q^{11} + 6 q^{13} - q^{16} - q^{17} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display