Properties

Label 249777.t
Number of curves $1$
Conductor $249777$
CM no
Rank $1$

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

Elliptic curves in class 249777.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
249777.t1 249777t1 \([0, 0, 1, -68121, 7078907]\) \(-2985984/121\) \(-1416656798696403\) \([]\) \(1741824\) \(1.6751\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 249777.t1 has rank \(1\).

Complex multiplication

The elliptic curves in class 249777.t do not have complex multiplication.

Modular form 249777.2.a.t

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