# Properties

 Label 7350.bg Number of curves 4 Conductor 7350 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("7350.bg1")

sage: E.isogeny_class()

## Elliptic curves in class 7350.bg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7350.bg1 7350bl4 [1, 0, 1, -1014326, -392004952]  144000
7350.bg2 7350bl2 [1, 0, 1, -64951, 6365048]  28800
7350.bg3 7350bl3 [1, 0, 1, -34326, -11764952]  72000
7350.bg4 7350bl1 [1, 0, 1, -3701, 117548]  14400 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form7350.2.a.bg

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} - q^{6} - q^{8} + q^{9} + 2q^{11} + q^{12} - 6q^{13} + q^{16} - 2q^{17} - q^{18} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 5 & 2 & 10 \\ 5 & 1 & 10 & 2 \\ 2 & 10 & 1 & 5 \\ 10 & 2 & 5 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 