Properties

Label 286110fc
Number of curves $1$
Conductor $286110$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("fc1")
 
E.isogeny_class()
 

Elliptic curves in class 286110fc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
286110.fc1 286110fc1 \([1, -1, 1, -7448018, 9512822481]\) \(-2596717791529849/718080000000\) \(-12635542344142080000000\) \([]\) \(32514048\) \(2.9567\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 286110fc1 has rank \(1\).

Complex multiplication

The elliptic curves in class 286110fc do not have complex multiplication.

Modular form 286110.2.a.fc

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{5} + 3 q^{7} + q^{8} - q^{10} - q^{11} - 5 q^{13} + 3 q^{14} + q^{16} + 7 q^{19} + O(q^{20})\) Copy content Toggle raw display