Properties

Label 41650.t
Number of curves $1$
Conductor $41650$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("t1")
 
E.isogeny_class()
 

Elliptic curves in class 41650.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
41650.t1 41650d1 \([1, 0, 1, 4874, -181352]\) \(341425679/578000\) \(-21684031250000\) \([]\) \(96768\) \(1.2440\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 41650.t1 has rank \(2\).

Complex multiplication

The elliptic curves in class 41650.t do not have complex multiplication.

Modular form 41650.2.a.t

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} - q^{8} - 2 q^{9} - 2 q^{11} + q^{12} - 4 q^{13} + q^{16} + q^{17} + 2 q^{18} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display