Properties

 Label 11760.cg Number of curves $2$ Conductor $11760$ CM no Rank $1$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("11760.cg1")

sage: E.isogeny_class()

Elliptic curves in class 11760.cg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11760.cg1 11760cq1 [0, 1, 0, -240, 468] [2] 4608 $$\Gamma_0(N)$$-optimal
11760.cg2 11760cq2 [0, 1, 0, 880, 4500] [2] 9216

Rank

sage: E.rank()

The elliptic curves in class 11760.cg have rank $$1$$.

Modular form 11760.2.a.cg

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} + q^{9} - 2q^{11} + 2q^{13} + q^{15} - 4q^{17} + O(q^{20})$$

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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with LMFDB labels.