# Properties

 Label 23064m Number of curves $6$ Conductor $23064$ CM no Rank $0$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 23064m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23064.i5 23064m1 $$[0, 1, 0, 641, -7510]$$ $$2048/3$$ $$-42600176688$$ $$[2]$$ $$14400$$ $$0.72507$$ $$\Gamma_0(N)$$-optimal
23064.i4 23064m2 $$[0, 1, 0, -4164, -78624]$$ $$35152/9$$ $$2044808481024$$ $$[2, 2]$$ $$28800$$ $$1.0716$$
23064.i3 23064m3 $$[0, 1, 0, -23384, 1305216]$$ $$1556068/81$$ $$73613105316864$$ $$[2, 2]$$ $$57600$$ $$1.4182$$
23064.i2 23064m4 $$[0, 1, 0, -61824, -5936880]$$ $$28756228/3$$ $$2726411308032$$ $$[2]$$ $$57600$$ $$1.4182$$
23064.i6 23064m5 $$[0, 1, 0, 15056, 5210720]$$ $$207646/6561$$ $$-11925323061331968$$ $$[2]$$ $$115200$$ $$1.7648$$
23064.i1 23064m6 $$[0, 1, 0, -369344, 86272992]$$ $$3065617154/9$$ $$16358467848192$$ $$[2]$$ $$115200$$ $$1.7648$$

## Rank

sage: E.rank()

The elliptic curves in class 23064m have rank $$0$$.

## Complex multiplication

The elliptic curves in class 23064m do not have complex multiplication.

## Modular form 23064.2.a.m

sage: E.q_eigenform(10)

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

## 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 Cremona numbering.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.