Properties

Label 102550z
Number of curves $1$
Conductor $102550$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("z1")
 
E.isogeny_class()
 

Elliptic curves in class 102550z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
102550.w1 102550z1 \([1, 0, 0, -3513, -5582983]\) \(-12274557745/34460475392\) \(-13461123200000000\) \([]\) \(836160\) \(1.7738\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 102550z1 has rank \(2\).

Complex multiplication

The elliptic curves in class 102550z do not have complex multiplication.

Modular form 102550.2.a.z

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