# Properties

 Label 29624.g Number of curves $4$ Conductor $29624$ CM no Rank $0$ Graph # Learn more

Show commands: SageMath
sage: E = EllipticCurve("g1")

sage: E.isogeny_class()

## Elliptic curves in class 29624.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
29624.g1 29624n4 $$[0, 0, 0, -158171, -24212330]$$ $$1443468546/7$$ $$2122242504704$$ $$$$ $$101376$$ $$1.5657$$
29624.g2 29624n3 $$[0, 0, 0, -31211, 1679046]$$ $$11090466/2401$$ $$727929179113472$$ $$$$ $$101376$$ $$1.5657$$
29624.g3 29624n2 $$[0, 0, 0, -10051, -365010]$$ $$740772/49$$ $$7427848766464$$ $$[2, 2]$$ $$50688$$ $$1.2191$$
29624.g4 29624n1 $$[0, 0, 0, 529, -24334]$$ $$432/7$$ $$-265280313088$$ $$$$ $$25344$$ $$0.87257$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 29624.2.a.g

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 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. 