# Properties

 Label 30345r Number of curves 2 Conductor 30345 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("30345.h1")

sage: E.isogeny_class()

## Elliptic curves in class 30345r

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
30345.h2 30345r1 [1, 1, 1, 45, -48] [2] 6144 $$\Gamma_0(N)$$-optimal
30345.h1 30345r2 [1, 1, 1, -210, -660] [2] 12288

## Rank

sage: E.rank()

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

## Modular form 30345.2.a.h

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 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.