# Properties

 Label 30015m Number of curves 2 Conductor 30015 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("30015.d1")
sage: E.isogeny_class()

## Elliptic curves in class 30015m

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
30015.d1 30015m1 [1, -1, 1, -3362, -74176] 2 13824 $$\Gamma_0(N)$$-optimal
30015.d2 30015m2 [1, -1, 1, -3137, -84706] 2 27648

## Rank

sage: E.rank()

The elliptic curves in class 30015m have rank $$0$$.

## Modular form 30015.2.a.d

sage: E.q_eigenform(10)
$$q - q^{2} - q^{4} + q^{5} + 3q^{8} - q^{10} - 2q^{11} + 2q^{13} - q^{16} + 4q^{17} + O(q^{20})$$

## 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. 