# Properties

 Label 7350.bv Number of curves 2 Conductor 7350 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("7350.bv1")

sage: E.isogeny_class()

## Elliptic curves in class 7350.bv

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7350.bv1 7350bo1 [1, 1, 1, -1103138, 446506031] [] 181440 $$\Gamma_0(N)$$-optimal
7350.bv2 7350bo2 [1, 1, 1, 2112487, 2272981031] [] 544320

## Rank

sage: E.rank()

The elliptic curves in class 7350.bv have rank $$0$$.

## Modular form7350.2.a.bv

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} - q^{6} + q^{8} + q^{9} - q^{12} - 5q^{13} + q^{16} + 6q^{17} + q^{18} - 7q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 