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Properties

Label 400710z
Number of curves $1$
Conductor $400710$
CM no
Rank $0$

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

Rank

Copy content sage:E.rank()
 

The elliptic curve 400710z1 has rank \(0\).

Complex multiplication

The elliptic curves in class 400710z do not have complex multiplication.

Modular form 400710.2.a.z

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} + 3 q^{7} - q^{8} + q^{9} - q^{10} + q^{11} + q^{12} - q^{13} - 3 q^{14} + q^{15} + q^{16} - q^{17} - q^{18} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 400710z

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
400710.z1 400710z1 \([1, 0, 1, -312273, 67140028]\) \(-71581931663761/199800\) \(-9399767023800\) \([]\) \(2916000\) \(1.7215\) \(\Gamma_0(N)\)-optimal