# Properties

 Label 23520.m Number of curves $4$ Conductor $23520$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("m1")

sage: E.isogeny_class()

## Elliptic curves in class 23520.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23520.m1 23520bf4 $$[0, -1, 0, -5000940016, 136122808277716]$$ $$229625675762164624948320008/9568125$$ $$576348333120000$$ $$[4]$$ $$10321920$$ $$3.7329$$
23520.m2 23520bf3 $$[0, -1, 0, -313630641, 2111674775841]$$ $$7079962908642659949376/100085966990454375$$ $$48230457059164023866880000$$ $$[2]$$ $$10321920$$ $$3.7329$$
23520.m3 23520bf1 $$[0, -1, 0, -312558766, 2126996800216]$$ $$448487713888272974160064/91549016015625$$ $$689321611854225000000$$ $$[2, 2]$$ $$5160960$$ $$3.3864$$ $$\Gamma_0(N)$$-optimal
23520.m4 23520bf2 $$[0, -1, 0, -311487136, 2142304820440]$$ $$-55486311952875723077768/801237030029296875$$ $$-48263544497109375000000000$$ $$[2]$$ $$10321920$$ $$3.7329$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 23520.2.a.m

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 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.