Properties

Label 61347u
Number of curves $1$
Conductor $61347$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 61347u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
61347.a1 61347u1 \([0, -1, 1, 620, 912]\) \(45056/27\) \(-15769185003\) \([]\) \(82944\) \(0.64606\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 61347u1 has rank \(2\).

Complex multiplication

The elliptic curves in class 61347u do not have complex multiplication.

Modular form 61347.2.a.u

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} - q^{3} + 2 q^{4} - 4 q^{5} + 2 q^{6} + q^{7} + q^{9} + 8 q^{10} - 2 q^{12} - 2 q^{14} + 4 q^{15} - 4 q^{16} - 4 q^{17} - 2 q^{18} - 3 q^{19} + O(q^{20})\) Copy content Toggle raw display