Properties

Label 78416.w
Number of curves $1$
Conductor $78416$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("w1")
 
E.isogeny_class()
 

Elliptic curves in class 78416.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
78416.w1 78416p1 \([0, 0, 0, -3211, -101062]\) \(-185193/116\) \(-2293390721024\) \([]\) \(215424\) \(1.0734\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 78416.w1 has rank \(0\).

Complex multiplication

The elliptic curves in class 78416.w do not have complex multiplication.

Modular form 78416.2.a.w

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