Properties

Label 28314.t
Number of curves $1$
Conductor $28314$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("t1")
 
E.isogeny_class()
 

Elliptic curves in class 28314.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28314.t1 28314n1 \([1, -1, 0, 291, -379]\) \(2803221/1664\) \(-1614577536\) \([]\) \(10752\) \(0.45620\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 28314.t1 has rank \(1\).

Complex multiplication

The elliptic curves in class 28314.t do not have complex multiplication.

Modular form 28314.2.a.t

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