# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("7350.cc1")

sage: E.isogeny_class()

## Elliptic curves in class 7350.cc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7350.cc1 7350cc4 [1, 1, 1, -40573, -3152269]  28800
7350.cc2 7350cc2 [1, 1, 1, -2598, 49881]  5760
7350.cc3 7350cc3 [1, 1, 1, -1373, -94669]  14400
7350.cc4 7350cc1 [1, 1, 1, -148, 881]  2880 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form7350.2.a.cc

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. 