# Properties

 Label 30800ca Number of curves 4 Conductor 30800 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("30800.u1")

sage: E.isogeny_class()

## Elliptic curves in class 30800ca

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
30800.u3 30800ca1 [0, 1, 0, -22408, -25132812]  331776 $$\Gamma_0(N)$$-optimal
30800.u2 30800ca2 [0, 1, 0, -1430408, -653100812]  663552
30800.u4 30800ca3 [0, 1, 0, 201592, 676883188]  995328
30800.u1 30800ca4 [0, 1, 0, -10446408, 12623939188]  1990656

## Rank

sage: E.rank()

The elliptic curves in class 30800ca have rank $$0$$.

## Modular form 30800.2.a.u

sage: E.q_eigenform(10)

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

## 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 Cremona numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 