# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("l1")

sage: E.isogeny_class()

## Elliptic curves in class 23520.l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23520.l1 23520bg4 $$[0, -1, 0, -54896, -4932360]$$ $$303735479048/105$$ $$6324810240$$ $$$$ $$73728$$ $$1.2365$$
23520.l2 23520bg3 $$[0, -1, 0, -7121, 117825]$$ $$82881856/36015$$ $$17355279298560$$ $$$$ $$73728$$ $$1.2365$$
23520.l3 23520bg1 $$[0, -1, 0, -3446, -75480]$$ $$601211584/11025$$ $$83013134400$$ $$[2, 2]$$ $$36864$$ $$0.88997$$ $$\Gamma_0(N)$$-optimal
23520.l4 23520bg2 $$[0, -1, 0, -16, -222284]$$ $$-8/354375$$ $$-21346234560000$$ $$$$ $$73728$$ $$1.2365$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 23520.2.a.l

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. 