# Properties

 Label 23520br Number of curves $4$ Conductor $23520$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("br1")

sage: E.isogeny_class()

## Elliptic curves in class 23520br

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23520.ba3 23520br1 $$[0, 1, 0, -312558766, -2126996800216]$$ $$448487713888272974160064/91549016015625$$ $$689321611854225000000$$ $$[2, 2]$$ $$5160960$$ $$3.3864$$ $$\Gamma_0(N)$$-optimal
23520.ba4 23520br2 $$[0, 1, 0, -311487136, -2142304820440]$$ $$-55486311952875723077768/801237030029296875$$ $$-48263544497109375000000000$$ $$[2]$$ $$10321920$$ $$3.7329$$
23520.ba2 23520br3 $$[0, 1, 0, -313630641, -2111674775841]$$ $$7079962908642659949376/100085966990454375$$ $$48230457059164023866880000$$ $$[4]$$ $$10321920$$ $$3.7329$$
23520.ba1 23520br4 $$[0, 1, 0, -5000940016, -136122808277716]$$ $$229625675762164624948320008/9568125$$ $$576348333120000$$ $$[2]$$ $$10321920$$ $$3.7329$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 23520.2.a.br

sage: E.q_eigenform(10)

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

## 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.