# Properties

 Label 7350i Number of curves $6$ Conductor $7350$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("7350.f1")

sage: E.isogeny_class()

## Elliptic curves in class 7350i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7350.f5 7350i1 [1, 1, 0, -4925, -295875] [2] 24576 $$\Gamma_0(N)$$-optimal
7350.f4 7350i2 [1, 1, 0, -102925, -12741875] [2, 2] 49152
7350.f1 7350i3 [1, 1, 0, -1646425, -813818375] [2] 98304
7350.f3 7350i4 [1, 1, 0, -127425, -6249375] [2, 2] 98304
7350.f2 7350i5 [1, 1, 0, -1119675, 451177875] [2] 196608
7350.f6 7350i6 [1, 1, 0, 472825, -47666625] [2] 196608

## Rank

sage: E.rank()

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

## Modular form7350.2.a.f

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} + q^{6} - q^{8} + q^{9} - 4q^{11} - q^{12} + 6q^{13} + q^{16} + 2q^{17} - q^{18} + 4q^{19} + O(q^{20})$$

## 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 Cremona numbering.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.