Properties

Label 64715.b
Number of curves $1$
Conductor $64715$
CM no
Rank $1$

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

Elliptic curves in class 64715.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
64715.b1 64715g1 \([1, 1, 1, -78105, -8656148]\) \(-28498608725272729/882735153125\) \(-1632177298128125\) \([]\) \(252000\) \(1.6960\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 64715.b1 has rank \(1\).

Complex multiplication

The elliptic curves in class 64715.b do not have complex multiplication.

Modular form 64715.2.a.b

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