# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("30345.u1")

sage: E.isogeny_class()

## Elliptic curves in class 30345a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
30345.u2 30345a1 [1, 1, 0, 33505932, -189536694237] [2] 5806080 $$\Gamma_0(N)$$-optimal
30345.u1 30345a2 [1, 1, 0, -361520943, -2343460232862] [2] 11612160

## Rank

sage: E.rank()

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

## Modular form 30345.2.a.u

sage: E.q_eigenform(10)

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

## 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.