# Properties

 Label 4704.m Number of curves $4$ Conductor $4704$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("m1")

sage: E.isogeny_class()

## Elliptic curves in class 4704.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4704.m1 4704u3 $$[0, -1, 0, -10992, 447252]$$ $$2438569736/21$$ $$1264962048$$ $$$$ $$6144$$ $$0.91432$$
4704.m2 4704u2 $$[0, -1, 0, -2417, -37407]$$ $$3241792/567$$ $$273231802368$$ $$$$ $$6144$$ $$0.91432$$
4704.m3 4704u1 $$[0, -1, 0, -702, 6840]$$ $$5088448/441$$ $$3320525376$$ $$[2, 2]$$ $$3072$$ $$0.56775$$ $$\Gamma_0(N)$$-optimal
4704.m4 4704u4 $$[0, -1, 0, 768, 30360]$$ $$830584/7203$$ $$-433881982464$$ $$$$ $$6144$$ $$0.91432$$

## Rank

sage: E.rank()

The elliptic curves in class 4704.m have rank $$1$$.

## Complex multiplication

The elliptic curves in class 4704.m do not have complex multiplication.

## Modular form4704.2.a.m

sage: E.q_eigenform(10)

$$q - q^{3} + 2q^{5} + q^{9} - 4q^{11} + 6q^{13} - 2q^{15} + 2q^{17} - 4q^{19} + O(q^{20})$$ ## 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. 