# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("7350.bc1")

sage: E.isogeny_class()

## Elliptic curves in class 7350.bc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7350.bc1 7350bh2 [1, 0, 1, -9270826, 9492495548]  627200
7350.bc2 7350bh1 [1, 0, 1, -2410826, -1291424452]  313600 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form7350.2.a.bc

sage: E.q_eigenform(10)

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

## 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 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. 