# Properties

 Label 23120bj Number of curves 4 Conductor 23120 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("23120.i1")

sage: E.isogeny_class()

## Elliptic curves in class 23120bj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
23120.i3 23120bj1 [0, 1, 0, -385, -2130] [2] 9216 $$\Gamma_0(N)$$-optimal
23120.i4 23120bj2 [0, 1, 0, 1060, -13112] [2] 18432
23120.i1 23120bj3 [0, 1, 0, -11945, 498418] [2] 27648
23120.i2 23120bj4 [0, 1, 0, -10500, 625000] [2] 55296

## Rank

sage: E.rank()

The elliptic curves in class 23120bj have rank $$1$$.

## Modular form 23120.2.a.i

sage: E.q_eigenform(10)

$$q - 2q^{3} + q^{5} + 2q^{7} + q^{9} + 2q^{13} - 2q^{15} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.