# Properties

 Label 3150.be Number of curves 2 Conductor 3150 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("3150.be1")

sage: E.isogeny_class()

## Elliptic curves in class 3150.be

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3150.be1 3150bo1 [1, -1, 1, -1535, -22633]  2560 $$\Gamma_0(N)$$-optimal
3150.be2 3150bo2 [1, -1, 1, -635, -49633]  5120

## Rank

sage: E.rank()

The elliptic curves in class 3150.be have rank $$0$$.

## Modular form3150.2.a.be

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - q^{7} + q^{8} + 2q^{11} - 2q^{13} - q^{14} + q^{16} + 8q^{17} - 2q^{19} + O(q^{20})$$

## 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. 