# Properties

 Label 23520.j Number of curves $2$ Conductor $23520$ CM no Rank $0$ Graph # Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("j1")

sage: E.isogeny_class()

## Elliptic curves in class 23520.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23520.j1 23520b1 $$[0, -1, 0, -10306, -329300]$$ $$16079333824/2953125$$ $$22235661000000$$ $$$$ $$55296$$ $$1.2795$$ $$\Gamma_0(N)$$-optimal
23520.j2 23520b2 $$[0, -1, 0, 20319, -1940175]$$ $$1925134784/4465125$$ $$-2151700443648000$$ $$$$ $$110592$$ $$1.6261$$

## Rank

sage: E.rank()

The elliptic curves in class 23520.j have rank $$0$$.

## Complex multiplication

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

## Modular form 23520.2.a.j

sage: E.q_eigenform(10)

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

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 