Properties

Label 55470.v
Number of curves $1$
Conductor $55470$
CM no
Rank $1$

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

Elliptic curves in class 55470.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
55470.v1 55470u1 \([1, 1, 1, 222305182134, 266453215936879959]\) \(192203697666261893287480365959/4963160303408775168000000000\) \(-31373938148231860089343967232000000000\) \([]\) \(1974551040\) \(5.8751\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 55470.v1 has rank \(1\).

Complex multiplication

The elliptic curves in class 55470.v do not have complex multiplication.

Modular form 55470.2.a.v

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} + 3 q^{7} + q^{8} + q^{9} - q^{10} + 4 q^{11} - q^{12} - 3 q^{13} + 3 q^{14} + q^{15} + q^{16} + q^{18} - 7 q^{19} + O(q^{20})\) Copy content Toggle raw display