Properties

Label 45486i
Number of curves $1$
Conductor $45486$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 45486i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
45486.o1 45486i1 \([1, -1, 0, 531, 119461]\) \(62851031/23514624\) \(-6188320083456\) \([]\) \(82944\) \(1.1336\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 45486i1 has rank \(1\).

Complex multiplication

The elliptic curves in class 45486i do not have complex multiplication.

Modular form 45486.2.a.i

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