# Properties

 Label 4560g Number of curves $4$ Conductor $4560$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 4560g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4560.bb4 4560g1 $$[0, 1, 0, -95, -732]$$ $$-5988775936/9774075$$ $$-156385200$$ $$$$ $$1024$$ $$0.26330$$ $$\Gamma_0(N)$$-optimal
4560.bb3 4560g2 $$[0, 1, 0, -1900, -32500]$$ $$2964647793616/2030625$$ $$519840000$$ $$[2, 2]$$ $$2048$$ $$0.60988$$
4560.bb1 4560g3 $$[0, 1, 0, -30400, -2050300]$$ $$3034301922374404/1425$$ $$1459200$$ $$$$ $$4096$$ $$0.95645$$
4560.bb2 4560g4 $$[0, 1, 0, -2280, -18972]$$ $$1280615525284/601171875$$ $$615600000000$$ $$$$ $$4096$$ $$0.95645$$

## Rank

sage: E.rank()

The elliptic curves in class 4560g have rank $$1$$.

## Complex multiplication

The elliptic curves in class 4560g do not have complex multiplication.

## Modular form4560.2.a.g

sage: E.q_eigenform(10)

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

## 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 Cremona numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with Cremona labels. 