Properties

Label 111573t
Number of curves $1$
Conductor $111573$
CM no
Rank $1$

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

Elliptic curves in class 111573t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
111573.p1 111573t1 \([1, -1, 1, -106222577, 421406015118]\) \(4505721246665691247/253\) \(7442698214259\) \([]\) \(6773760\) \(2.8580\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 111573t1 has rank \(1\).

Complex multiplication

The elliptic curves in class 111573t do not have complex multiplication.

Modular form 111573.2.a.t

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