# Properties

 Label 242760.cr Number of curves $6$ Conductor $242760$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("242760.cr1")

sage: E.isogeny_class()

## Elliptic curves in class 242760.cr

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
242760.cr1 242760cr6 [0, 1, 0, -3028816, -2029849696]  5242880
242760.cr2 242760cr4 [0, 1, 0, -196616, -29183616] [2, 2] 2621440
242760.cr3 242760cr2 [0, 1, 0, -52116, 4109184] [2, 2] 1310720
242760.cr4 242760cr1 [0, 1, 0, -50671, 4373330]  655360 $$\Gamma_0(N)$$-optimal
242760.cr5 242760cr3 [0, 1, 0, 69264, 20519760]  2621440
242760.cr6 242760cr5 [0, 1, 0, 323584, -156944736]  5242880

## Rank

sage: E.rank()

The elliptic curves in class 242760.cr have rank $$0$$.

## Modular form 242760.2.a.cr

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} + q^{7} + q^{9} + 4q^{11} - 2q^{13} - q^{15} - 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 