Properties

Label 77315a
Number of curves $1$
Conductor $77315$
CM no
Rank $2$

Related objects

Downloads

Learn more

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

Elliptic curves in class 77315a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
77315.c1 77315a1 \([0, 1, 1, -11781, 723795]\) \(-16777216/11515\) \(-124122664513435\) \([]\) \(229632\) \(1.4047\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 77315a1 has rank \(2\).

Complex multiplication

The elliptic curves in class 77315a do not have complex multiplication.

Modular form 77315.2.a.a

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