Properties

Label 20286.e
Number of curves $1$
Conductor $20286$
CM no
Rank $1$

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

Elliptic curves in class 20286.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20286.e1 20286d1 \([1, -1, 0, -101129541, -391414687147]\) \(-1008050316336685251/23552\) \(-2672411951010816\) \([]\) \(1411200\) \(2.9336\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 20286.e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 20286.e do not have complex multiplication.

Modular form 20286.2.a.e

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