Properties

Label 217672.v
Number of curves $1$
Conductor $217672$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("v1")
 
E.isogeny_class()
 

Elliptic curves in class 217672.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
217672.v1 217672v1 \([0, 0, 0, -1422811, 662762399]\) \(-4124632486295808/70140333767\) \(-5416863908632952048\) \([]\) \(6289920\) \(2.3932\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 217672.v1 has rank \(0\).

Complex multiplication

The elliptic curves in class 217672.v do not have complex multiplication.

Modular form 217672.2.a.v

sage: E.q_eigenform(10)
 
\(q + 3 q^{3} - 2 q^{5} + q^{7} + 6 q^{9} - 2 q^{11} - 6 q^{15} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display