# Properties

 Label 9464.c Number of curves $4$ Conductor $9464$ CM no Rank $0$ Graph # Learn more

Show commands for: SageMath
sage: E = EllipticCurve("c1")

sage: E.isogeny_class()

## Elliptic curves in class 9464.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9464.c1 9464d4 $$[0, 0, 0, -50531, 4372030]$$ $$1443468546/7$$ $$69197133824$$ $$$$ $$18432$$ $$1.2804$$
9464.c2 9464d3 $$[0, 0, 0, -9971, -303186]$$ $$11090466/2401$$ $$23734616901632$$ $$$$ $$18432$$ $$1.2804$$
9464.c3 9464d2 $$[0, 0, 0, -3211, 65910]$$ $$740772/49$$ $$242189968384$$ $$[2, 2]$$ $$9216$$ $$0.93387$$
9464.c4 9464d1 $$[0, 0, 0, 169, 4394]$$ $$432/7$$ $$-8649641728$$ $$$$ $$4608$$ $$0.58729$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 9464.c have rank $$0$$.

## Complex multiplication

The elliptic curves in class 9464.c do not have complex multiplication.

## Modular form9464.2.a.c

sage: E.q_eigenform(10)

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