# Properties

 Label 9240.c Number of curves $4$ Conductor $9240$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 9240.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9240.c1 9240b3 $$[0, -1, 0, -16294696, -22417652180]$$ $$233632133015204766393938/29145526885986328125$$ $$59690039062500000000000$$ $$$$ $$983040$$ $$3.0999$$
9240.c2 9240b2 $$[0, -1, 0, -4070176, 2799087676]$$ $$7282213870869695463556/912102595400390625$$ $$933993057690000000000$$ $$[2, 2]$$ $$491520$$ $$2.7534$$
9240.c3 9240b1 $$[0, -1, 0, -3938956, 3010246900]$$ $$26401417552259125806544/507547744790625$$ $$129932222666400000$$ $$$$ $$245760$$ $$2.4068$$ $$\Gamma_0(N)$$-optimal
9240.c4 9240b4 $$[0, -1, 0, 6054824, 14499537676]$$ $$11986661998777424518222/51295853620928503125$$ $$-105053908215661574400000$$ $$$$ $$983040$$ $$3.0999$$

## Rank

sage: E.rank()

The elliptic curves in class 9240.c have rank $$0$$.

## Complex multiplication

The elliptic curves in class 9240.c do not have complex multiplication.

## Modular form9240.2.a.c

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} + q^{7} + q^{9} - q^{11} + 2 q^{13} + q^{15} - 6 q^{17} - 4 q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels. 