# Properties

 Label 29400q Number of curves $4$ Conductor $29400$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("q1")

sage: E.isogeny_class()

## Elliptic curves in class 29400q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
29400.j4 29400q1 [0, -1, 0, 10617, -128988] [2] 73728 $$\Gamma_0(N)$$-optimal
29400.j3 29400q2 [0, -1, 0, -44508, -1010988] [2, 2] 147456
29400.j2 29400q3 [0, -1, 0, -412008, 101154012] [2] 294912
29400.j1 29400q4 [0, -1, 0, -559008, -160505988] [2] 294912

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 29400.2.a.q

sage: E.q_eigenform(10)

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

## 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.