# Properties

 Label 7350.m Number of curves 2 Conductor 7350 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("7350.m1")

sage: E.isogeny_class()

## Elliptic curves in class 7350.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7350.m1 7350m2 [1, 1, 0, -189200, -27756000]  89600
7350.m2 7350m1 [1, 1, 0, -49200, 3744000]  44800 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 7350.m have rank $$1$$.

## Modular form7350.2.a.m

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. 