Properties

Label 212415j
Number of curves $1$
Conductor $212415$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 212415j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
212415.b1 212415j1 \([0, -1, 1, -89686, 17066496]\) \(-1376628736/1366875\) \(-79216288144126875\) \([]\) \(3311616\) \(1.9384\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 212415j1 has rank \(1\).

Complex multiplication

The elliptic curves in class 212415j do not have complex multiplication.

Modular form 212415.2.a.j

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