Properties

Label 212940.z
Number of curves $1$
Conductor $212940$
CM no
Rank $2$

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

Elliptic curves in class 212940.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
212940.z1 212940n1 \([0, 0, 0, 12168, 54756]\) \(37380096/21875\) \(-116597426400000\) \([]\) \(622080\) \(1.3886\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 212940.z1 has rank \(2\).

Complex multiplication

The elliptic curves in class 212940.z do not have complex multiplication.

Modular form 212940.2.a.z

sage: E.q_eigenform(10)
 
\(q + q^{5} - q^{7} - 3 q^{11} - 7 q^{17} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display