Properties

Label 77315.b
Number of curves $1$
Conductor $77315$
CM no
Rank $1$

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Show commands: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 77315.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
77315.b1 77315e1 \([1, 0, 0, -101660, -11930933]\) \(4879681/245\) \(5833765232131445\) \([]\) \(577536\) \(1.7838\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 77315.b1 has rank \(1\).

Complex multiplication

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

Modular form 77315.2.a.b

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