Properties

Label 77763r
Number of curves $1$
Conductor $77763$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 77763r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
77763.be1 77763r1 \([0, -1, 1, -2497056, -1771459621]\) \(-98867482624/20696067\) \(-360448379905851288387\) \([]\) \(7603200\) \(2.6662\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 77763r1 has rank \(1\).

Complex multiplication

The elliptic curves in class 77763r do not have complex multiplication.

Modular form 77763.2.a.r

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