Properties

Label 1748.c
Number of curves $1$
Conductor $1748$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 1748.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1748.c1 1748a1 \([0, -1, 0, -90, 361]\) \(-5095042816/8303\) \(-132848\) \([]\) \(360\) \(-0.12011\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1748.c1 has rank \(2\).

Complex multiplication

The elliptic curves in class 1748.c do not have complex multiplication.

Modular form 1748.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{3} - 4 q^{5} - 2 q^{7} - 2 q^{9} - 6 q^{11} - 3 q^{13} + 4 q^{15} - 4 q^{17} - q^{19} + O(q^{20})\) Copy content Toggle raw display