Properties

Label 19074e
Number of curves 1
Conductor 19074
CM no
Rank 1

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Show commands for: SageMath
sage: E = EllipticCurve("19074.c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 19074e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
19074.c1 19074e1 [1, 1, 0, -475844, -126553458] [] 190944 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 19074e1 has rank \(1\).

Modular form 19074.2.a.c

sage: E.q_eigenform(10)
 
\( q - q^{2} - q^{3} + q^{4} + 2q^{5} + q^{6} - 2q^{7} - q^{8} + q^{9} - 2q^{10} + q^{11} - q^{12} + 3q^{13} + 2q^{14} - 2q^{15} + q^{16} - q^{18} - 5q^{19} + O(q^{20}) \)