Properties

Label 71478a
Number of curves $1$
Conductor $71478$
CM no
Rank $1$

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

Elliptic curves in class 71478a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
71478.g1 71478a1 \([1, -1, 0, 798645, -85857211]\) \(8869743/5632\) \(-35771433732723009024\) \([]\) \(2298240\) \(2.4410\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 71478a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 71478a do not have complex multiplication.

Modular form 71478.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - 4 q^{7} - q^{8} + q^{10} - q^{11} + 2 q^{13} + 4 q^{14} + q^{16} + 3 q^{17} + O(q^{20})\) Copy content Toggle raw display