# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("e1")

sage: E.isogeny_class()

## Elliptic curves in class 23520.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23520.e1 23520bh4 $$[0, -1, 0, -4116016, -3212760284]$$ $$128025588102048008/7875$$ $$474360768000$$ $$[2]$$ $$294912$$ $$2.1489$$
23520.e2 23520bh3 $$[0, -1, 0, -288136, -37311560]$$ $$43919722445768/15380859375$$ $$926485875000000000$$ $$[2]$$ $$294912$$ $$2.1489$$
23520.e3 23520bh1 $$[0, -1, 0, -257266, -50128784]$$ $$250094631024064/62015625$$ $$466948881000000$$ $$[2, 2]$$ $$147456$$ $$1.8023$$ $$\Gamma_0(N)$$-optimal
23520.e4 23520bh2 $$[0, -1, 0, -226641, -62544159]$$ $$-2671731885376/1969120125$$ $$-948899895648768000$$ $$[2]$$ $$294912$$ $$2.1489$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 23520.2.a.e

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} + q^{9} - 4q^{11} + 2q^{13} + q^{15} + 2q^{17} + 8q^{19} + O(q^{20})$$

## 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.