# Properties

 Label 3360.c Number of curves $4$ Conductor $3360$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 3360.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3360.c1 3360c2 $$[0, -1, 0, -317521, -68760575]$$ $$864335783029582144/59535$$ $$243855360$$ $$$$ $$15360$$ $$1.5103$$
3360.c2 3360c3 $$[0, -1, 0, -22296, -786060]$$ $$2394165105226952/854262178245$$ $$437382235261440$$ $$$$ $$15360$$ $$1.5103$$
3360.c3 3360c1 $$[0, -1, 0, -19846, -1069280]$$ $$13507798771700416/3544416225$$ $$226842638400$$ $$[2, 2]$$ $$7680$$ $$1.1637$$ $$\Gamma_0(N)$$-optimal
3360.c4 3360c4 $$[0, -1, 0, -17416, -1343384]$$ $$-1141100604753992/875529151875$$ $$-448270925760000$$ $$$$ $$15360$$ $$1.5103$$

## Rank

sage: E.rank()

The elliptic curves in class 3360.c have rank $$1$$.

## Complex multiplication

The elliptic curves in class 3360.c do not have complex multiplication.

## Modular form3360.2.a.c

sage: E.q_eigenform(10)

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