Properties

Label 100026.e
Number of curves $1$
Conductor $100026$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 100026.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
100026.e1 100026d1 \([1, -1, 1, -6926, 232733]\) \(-50394699308953/2458238976\) \(-1792056213504\) \([]\) \(314496\) \(1.1130\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 100026.e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 100026.e do not have complex multiplication.

Modular form 100026.2.a.e

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