# Properties

 Label 7623f Number of curves 3 Conductor 7623 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("7623.i1")

sage: E.isogeny_class()

## Elliptic curves in class 7623f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7623.i1 7623f1 [0, 0, 1, -97284, 11679192] [] 24000 $$\Gamma_0(N)$$-optimal
7623.i2 7623f2 [0, 0, 1, -53724, 22160817] [] 72000
7623.i3 7623f3 [0, 0, 1, 479886, -573614748] [] 216000

## Rank

sage: E.rank()

The elliptic curves in class 7623f have rank $$1$$.

## Modular form7623.2.a.i

sage: E.q_eigenform(10)

$$q - 2q^{4} - 3q^{5} - q^{7} + 4q^{13} + 4q^{16} - 6q^{17} - 2q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 