# Properties

 Label 3600.u Number of curves $8$ Conductor $3600$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("u1")

sage: E.isogeny_class()

## Elliptic curves in class 3600.u

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3600.u1 3600bf7 $$[0, 0, 0, -7776075, -8346199750]$$ $$1114544804970241/405$$ $$18895680000000$$ $$[2]$$ $$49152$$ $$2.3380$$
3600.u2 3600bf5 $$[0, 0, 0, -486075, -130369750]$$ $$272223782641/164025$$ $$7652750400000000$$ $$[2, 2]$$ $$24576$$ $$1.9915$$
3600.u3 3600bf8 $$[0, 0, 0, -396075, -180139750]$$ $$-147281603041/215233605$$ $$-10041939074880000000$$ $$[2]$$ $$49152$$ $$2.3380$$
3600.u4 3600bf4 $$[0, 0, 0, -288075, 59512250]$$ $$56667352321/15$$ $$699840000000$$ $$[4]$$ $$12288$$ $$1.6449$$
3600.u5 3600bf3 $$[0, 0, 0, -36075, -1219750]$$ $$111284641/50625$$ $$2361960000000000$$ $$[2, 2]$$ $$12288$$ $$1.6449$$
3600.u6 3600bf2 $$[0, 0, 0, -18075, 922250]$$ $$13997521/225$$ $$10497600000000$$ $$[2, 2]$$ $$6144$$ $$1.2983$$
3600.u7 3600bf1 $$[0, 0, 0, -75, 40250]$$ $$-1/15$$ $$-699840000000$$ $$[2]$$ $$3072$$ $$0.95175$$ $$\Gamma_0(N)$$-optimal
3600.u8 3600bf6 $$[0, 0, 0, 125925, -9157750]$$ $$4733169839/3515625$$ $$-164025000000000000$$ $$[2]$$ $$24576$$ $$1.9915$$

## Rank

sage: E.rank()

The elliptic curves in class 3600.u have rank $$1$$.

## Complex multiplication

The elliptic curves in class 3600.u do not have complex multiplication.

## Modular form3600.2.a.u

sage: E.q_eigenform(10)

$$q - 4 q^{11} + 2 q^{13} + 2 q^{17} - 4 q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 16 & 4 & 8 & 16 & 8 \\ 2 & 1 & 2 & 8 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 16 & 4 & 8 & 16 & 8 \\ 16 & 8 & 16 & 1 & 4 & 2 & 4 & 8 \\ 4 & 2 & 4 & 4 & 1 & 2 & 4 & 2 \\ 8 & 4 & 8 & 2 & 2 & 1 & 2 & 4 \\ 16 & 8 & 16 & 4 & 4 & 2 & 1 & 8 \\ 8 & 4 & 8 & 8 & 2 & 4 & 8 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.