# Properties

 Label 29400.ce Number of curves $6$ Conductor $29400$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("ce1")

sage: E.isogeny_class()

## Elliptic curves in class 29400.ce

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
29400.ce1 29400n6 $$[0, -1, 0, -470808, 124497612]$$ $$3065617154/9$$ $$33882912000000$$ $$[2]$$ $$196608$$ $$1.8255$$
29400.ce2 29400n4 $$[0, -1, 0, -78808, -8488388]$$ $$28756228/3$$ $$5647152000000$$ $$[2]$$ $$98304$$ $$1.4789$$
29400.ce3 29400n3 $$[0, -1, 0, -29808, 1899612]$$ $$1556068/81$$ $$152473104000000$$ $$[2, 2]$$ $$98304$$ $$1.4789$$
29400.ce4 29400n2 $$[0, -1, 0, -5308, -109388]$$ $$35152/9$$ $$4235364000000$$ $$[2, 2]$$ $$49152$$ $$1.1323$$
29400.ce5 29400n1 $$[0, -1, 0, 817, -11388]$$ $$2048/3$$ $$-88236750000$$ $$[2]$$ $$24576$$ $$0.78575$$ $$\Gamma_0(N)$$-optimal
29400.ce6 29400n5 $$[0, -1, 0, 19192, 7485612]$$ $$207646/6561$$ $$-24700642848000000$$ $$[2]$$ $$196608$$ $$1.8255$$

## Rank

sage: E.rank()

The elliptic curves in class 29400.ce have rank $$0$$.

## Complex multiplication

The elliptic curves in class 29400.ce do not have complex multiplication.

## Modular form 29400.2.a.ce

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.