# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("i1")

sage: E.isogeny_class()

## Elliptic curves in class 23520.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23520.i1 23520bb4 $$[0, -1, 0, -23536, 1397656]$$ $$23937672968/45$$ $$2710632960$$ $$[2]$$ $$36864$$ $$1.0653$$
23520.i2 23520bb3 $$[0, -1, 0, -3936, -65484]$$ $$111980168/32805$$ $$1976051427840$$ $$[2]$$ $$36864$$ $$1.0653$$
23520.i3 23520bb1 $$[0, -1, 0, -1486, 21736]$$ $$48228544/2025$$ $$15247310400$$ $$[2, 2]$$ $$18432$$ $$0.71870$$ $$\Gamma_0(N)$$-optimal
23520.i4 23520bb2 $$[0, -1, 0, 719, 78625]$$ $$85184/5625$$ $$-2710632960000$$ $$[2]$$ $$36864$$ $$1.0653$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 23520.2.a.i

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} + q^{9} + 2q^{13} + q^{15} + 6q^{17} + O(q^{20})$$

## 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.