# Properties

 Label 310464cg Number of curves $4$ Conductor $310464$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("cg1")

sage: E.isogeny_class()

## Elliptic curves in class 310464cg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
310464.cg3 310464cg1 $$[0, 0, 0, -1035419196, 12823968186736]$$ $$87364831012240243408/1760913$$ $$2474421082988101632$$ $$$$ $$70778880$$ $$3.5128$$ $$\Gamma_0(N)$$-optimal
310464.cg2 310464cg2 $$[0, 0, 0, -1035454476, 12823050582160]$$ $$21843440425782779332/3100814593569$$ $$17428961010031308036440064$$ $$[2, 2]$$ $$141557760$$ $$3.8594$$
310464.cg4 310464cg3 $$[0, 0, 0, -942103596, 15229076163280]$$ $$-8226100326647904626/4152140742401883$$ $$-46676443833548108989181853696$$ $$$$ $$283115520$$ $$4.2060$$
310464.cg1 310464cg4 $$[0, 0, 0, -1129369836, 10358298308176]$$ $$14171198121996897746/4077720290568771$$ $$45839843569837850284168445952$$ $$$$ $$283115520$$ $$4.2060$$

## Rank

sage: E.rank()

The elliptic curves in class 310464cg have rank $$0$$.

## Complex multiplication

The elliptic curves in class 310464cg do not have complex multiplication.

## Modular form 310464.2.a.cg

sage: E.q_eigenform(10)

$$q - 2q^{5} - q^{11} - 6q^{13} - 2q^{17} + 8q^{19} + O(q^{20})$$ ## 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. 