Properties

Label 24646.a
Number of curves $1$
Conductor $24646$
CM no
Rank $3$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 24646.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
24646.a1 24646b1 \([1, 0, 1, -13, 12]\) \(217081801/49292\) \(49292\) \([]\) \(5392\) \(-0.38689\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 24646.a1 has rank \(3\).

Complex multiplication

The elliptic curves in class 24646.a do not have complex multiplication.

Modular form 24646.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} - 2 q^{3} + q^{4} - 4 q^{5} + 2 q^{6} - 2 q^{7} - q^{8} + q^{9} + 4 q^{10} - 4 q^{11} - 2 q^{12} - 5 q^{13} + 2 q^{14} + 8 q^{15} + q^{16} - 3 q^{17} - q^{18} - 7 q^{19} + O(q^{20})\) Copy content Toggle raw display