# Properties

 Label 23520.n Number of curves $4$ Conductor $23520$ CM no Rank $1$ Graph # Learn more about

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

sage: E.isogeny_class()

## Elliptic curves in class 23520.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23520.n1 23520l4 $$[0, -1, 0, -176465, 28591137]$$ $$1261112198464/675$$ $$325275955200$$ $$$$ $$110592$$ $$1.5386$$
23520.n2 23520l3 $$[0, -1, 0, -24320, -804600]$$ $$26410345352/10546875$$ $$635304600000000$$ $$$$ $$110592$$ $$1.5386$$
23520.n3 23520l1 $$[0, -1, 0, -11090, 444312]$$ $$20034997696/455625$$ $$3430644840000$$ $$[2, 2]$$ $$55296$$ $$1.1920$$ $$\Gamma_0(N)$$-optimal
23520.n4 23520l2 $$[0, -1, 0, 1160, 1360612]$$ $$2863288/13286025$$ $$-800300828275200$$ $$$$ $$110592$$ $$1.5386$$

## Rank

sage: E.rank()

The elliptic curves in class 23520.n have rank $$1$$.

## Complex multiplication

The elliptic curves in class 23520.n do not have complex multiplication.

## Modular form 23520.2.a.n

sage: E.q_eigenform(10)

$$q - q^{3} + q^{5} + q^{9} - 4q^{11} - 6q^{13} - q^{15} - 2q^{17} + 4q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 