Properties

Label 250470z
Number of curves $1$
Conductor $250470$
CM no
Rank $1$

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

Elliptic curves in class 250470z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
250470.z1 250470z1 \([1, -1, 0, -20726415, 38026317181]\) \(-6301258312598161/349801250000\) \(-54662610296830511250000\) \([]\) \(31933440\) \(3.1206\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 250470z1 has rank \(1\).

Complex multiplication

The elliptic curves in class 250470z do not have complex multiplication.

Modular form 250470.2.a.z

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} + q^{7} - q^{8} + q^{10} + 4 q^{13} - q^{14} + q^{16} + 4 q^{17} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display