# Properties

 Label 1800.m Number of curves $6$ Conductor $1800$ CM no Rank $1$ Graph # Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("m1")

sage: E.isogeny_class()

## Elliptic curves in class 1800.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1800.m1 1800s5 $$[0, 0, 0, -86475, 9787750]$$ $$3065617154/9$$ $$209952000000$$ $$$$ $$4096$$ $$1.4018$$
1800.m2 1800s3 $$[0, 0, 0, -14475, -670250]$$ $$28756228/3$$ $$34992000000$$ $$$$ $$2048$$ $$1.0552$$
1800.m3 1800s4 $$[0, 0, 0, -5475, 148750]$$ $$1556068/81$$ $$944784000000$$ $$[2, 2]$$ $$2048$$ $$1.0552$$
1800.m4 1800s2 $$[0, 0, 0, -975, -8750]$$ $$35152/9$$ $$26244000000$$ $$[2, 2]$$ $$1024$$ $$0.70867$$
1800.m5 1800s1 $$[0, 0, 0, 150, -875]$$ $$2048/3$$ $$-546750000$$ $$$$ $$512$$ $$0.36210$$ $$\Gamma_0(N)$$-optimal
1800.m6 1800s6 $$[0, 0, 0, 3525, 589750]$$ $$207646/6561$$ $$-153055008000000$$ $$$$ $$4096$$ $$1.4018$$

## Rank

sage: E.rank()

The elliptic curves in class 1800.m have rank $$1$$.

## Complex multiplication

The elliptic curves in class 1800.m do not have complex multiplication.

## Modular form1800.2.a.m

sage: E.q_eigenform(10)

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

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 