Properties

Label 398878.m
Number of curves $1$
Conductor $398878$
CM no
Rank $2$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 398878.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
398878.m1 398878m1 \([1, -1, 1, -7376961, 7682031825]\) \(2003092024307193/9529458688\) \(211214363724718538752\) \([]\) \(48522240\) \(2.7492\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 398878.m1 has rank \(2\).

Complex multiplication

The elliptic curves in class 398878.m do not have complex multiplication.

Modular form 398878.2.a.m

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