# Properties

 Label 30345f Number of curves 2 Conductor 30345 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("30345.e1")

sage: E.isogeny_class()

## Elliptic curves in class 30345f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
30345.e2 30345f1 [1, 1, 1, 111259, -114132166]  470016 $$\Gamma_0(N)$$-optimal
30345.e1 30345f2 [1, 1, 1, -2959366, -1875442666]  940032

## Rank

sage: E.rank()

The elliptic curves in class 30345f have rank $$0$$.

## Modular form 30345.2.a.e

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} - q^{4} - q^{5} + q^{6} + q^{7} + 3q^{8} + q^{9} + q^{10} - 2q^{11} + q^{12} - 4q^{13} - q^{14} + q^{15} - q^{16} - q^{18} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 