# Properties

 Label 29624n Number of curves $4$ Conductor $29624$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("n1")

sage: E.isogeny_class()

## Elliptic curves in class 29624n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
29624.g4 29624n1 [0, 0, 0, 529, -24334]  25344 $$\Gamma_0(N)$$-optimal
29624.g3 29624n2 [0, 0, 0, -10051, -365010] [2, 2] 50688
29624.g2 29624n3 [0, 0, 0, -31211, 1679046]  101376
29624.g1 29624n4 [0, 0, 0, -158171, -24212330]  101376

## Rank

sage: E.rank()

The elliptic curves in class 29624n have rank $$0$$.

## Complex multiplication

The elliptic curves in class 29624n do not have complex multiplication.

## Modular form 29624.2.a.n

sage: E.q_eigenform(10)

$$q - 2q^{5} + q^{7} - 3q^{9} + 4q^{11} + 2q^{13} + 6q^{17} - 8q^{19} + O(q^{20})$$

## 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. 