# Properties

 Label 7350.cz Number of curves $2$ Conductor $7350$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("cz1")

sage: E.isogeny_class()

## Elliptic curves in class 7350.cz

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7350.cz1 7350cr2 $$[1, 0, 0, -429388, 114549392]$$ $$-7620530425/526848$$ $$-605304105000000000$$ $$[]$$ $$155520$$ $$2.1630$$
7350.cz2 7350cr1 $$[1, 0, 0, 29987, 165017]$$ $$2595575/1512$$ $$-1737161015625000$$ $$[]$$ $$51840$$ $$1.6137$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 7350.cz do not have complex multiplication.

## Modular form7350.2.a.cz

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 