Properties

Label 1479.c
Number of curves 2
Conductor 1479
CM no
Rank 1
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath

sage: E = EllipticCurve("1479.c1")
sage: E.isogeny_class()

Elliptic curves in class 1479.c

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
1479.c1 1479f1 [0, 1, 1, -6070, 181852] 5 2400 \(\Gamma_0(N)\)-optimal
1479.c2 1479f2 [0, 1, 1, 39320, -6363488] 1 12000  

Rank

sage: E.rank()

The elliptic curves in class 1479.c have rank \(1\).

Modular form 1479.2.a.c

sage: E.q_eigenform(10)
\( q - 2q^{2} + q^{3} + 2q^{4} + q^{5} - 2q^{6} - 2q^{7} + q^{9} - 2q^{10} - 3q^{11} + 2q^{12} - q^{13} + 4q^{14} + q^{15} - 4q^{16} + q^{17} - 2q^{18} + 5q^{19} + O(q^{20}) \)

Isogeny matrix

sage: E.isogeny_class().matrix()

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels.