# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("g1")

sage: E.isogeny_class()

## Elliptic curves in class 23520.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23520.g1 23520bd4 $$[0, -1, 0, -7856, -265404]$$ $$890277128/15$$ $$903544320$$ $$$$ $$24576$$ $$0.84876$$
23520.g2 23520bd3 $$[0, -1, 0, -1976, 30360]$$ $$14172488/1875$$ $$112943040000$$ $$$$ $$24576$$ $$0.84876$$
23520.g3 23520bd1 $$[0, -1, 0, -506, -3744]$$ $$1906624/225$$ $$1694145600$$ $$[2, 2]$$ $$12288$$ $$0.50218$$ $$\Gamma_0(N)$$-optimal
23520.g4 23520bd2 $$[0, -1, 0, 719, -20159]$$ $$85184/405$$ $$-195165573120$$ $$$$ $$24576$$ $$0.84876$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 23520.2.a.g

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} + q^{9} - 2q^{13} + q^{15} - 6q^{17} - 4q^{19} + O(q^{20})$$ ## 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. 