# Properties

 Label 7350d Number of curves $2$ Conductor $7350$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("7350.o1")

sage: E.isogeny_class()

## Elliptic curves in class 7350d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7350.o1 7350d1 [1, 1, 0, -18400, 359500] [2] 32256 $$\Gamma_0(N)$$-optimal
7350.o2 7350d2 [1, 1, 0, 67350, 2846250] [2] 64512

## Rank

sage: E.rank()

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

## Modular form7350.2.a.o

sage: E.q_eigenform(10)

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

## 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 Cremona 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 Cremona labels.