Properties

Label 8048.c
Number of curves $1$
Conductor $8048$
CM no
Rank $2$

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

Elliptic curves in class 8048.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8048.c1 8048g1 \([0, -1, 0, -3360, 76096]\) \(-1024497361441/503\) \(-2060288\) \([]\) \(6400\) \(0.54631\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 8048.c1 has rank \(2\).

Complex multiplication

The elliptic curves in class 8048.c do not have complex multiplication.

Modular form 8048.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{3} - 4 q^{5} + 3 q^{7} - 2 q^{9} - 5 q^{11} + q^{13} + 4 q^{15} - 8 q^{19} + O(q^{20})\) Copy content Toggle raw display