Properties

Label 68970.m
Number of curves $1$
Conductor $68970$
CM no
Rank $1$

Related objects

Downloads

Learn more

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

Elliptic curves in class 68970.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
68970.m1 68970j1 \([1, 1, 0, 103255348, -2776077721776]\) \(4693907404762135439/131077531238400000\) \(-3399813583381222155878400000\) \([]\) \(37160640\) \(3.9629\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 68970.m1 has rank \(1\).

Complex multiplication

The elliptic curves in class 68970.m do not have complex multiplication.

Modular form 68970.2.a.m

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