# Properties

 Label 30345.g Number of curves 2 Conductor 30345 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("30345.g1")

sage: E.isogeny_class()

## Elliptic curves in class 30345.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
30345.g1 30345q2 [1, 1, 1, -4093169430, -93611649792600]  34467840
30345.g2 30345q1 [1, 1, 1, 258446625, -6603697742508]  17233920 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 30345.g have rank $$1$$.

## Modular form 30345.2.a.g

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 