# Properties

 Label 7623o Number of curves 2 Conductor 7623 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("7623.n1")

sage: E.isogeny_class()

## Elliptic curves in class 7623o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7623.n2 7623o1 [1, -1, 0, 3789, 339664]  17280 $$\Gamma_0(N)$$-optimal
7623.n1 7623o2 [1, -1, 0, -56106, 4735957]  34560

## Rank

sage: E.rank()

The elliptic curves in class 7623o have rank $$0$$.

## Modular form7623.2.a.n

sage: E.q_eigenform(10)

$$q + q^{2} - q^{4} + 2q^{5} + q^{7} - 3q^{8} + 2q^{10} - 4q^{13} + q^{14} - q^{16} + 4q^{17} + O(q^{20})$$

## 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. 