# Properties

 Label 30345.l Number of curves 4 Conductor 30345 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("30345.l1")

sage: E.isogeny_class()

## Elliptic curves in class 30345.l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
30345.l1 30345bf4 [1, 0, 0, -17687095, -28632233938] [2] 884736
30345.l2 30345bf3 [1, 0, 0, -1378825, -209447500] [2] 884736
30345.l3 30345bf2 [1, 0, 0, -1105720, -447212713] [2, 2] 442368
30345.l4 30345bf1 [1, 0, 0, -52315, -10471000] [4] 221184 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form 30345.2.a.l

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.