# Properties

 Label 1200.m Number of curves $4$ Conductor $1200$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 1200.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1200.m1 1200q4 $$[0, 1, 0, -331208, -73238412]$$ $$502270291349/1889568$$ $$15116544000000000$$ $$$$ $$9600$$ $$1.9639$$
1200.m2 1200q2 $$[0, 1, 0, -21208, 1181588]$$ $$131872229/18$$ $$144000000000$$ $$$$ $$1920$$ $$1.1592$$
1200.m3 1200q3 $$[0, 1, 0, -11208, -2198412]$$ $$-19465109/248832$$ $$-1990656000000000$$ $$$$ $$4800$$ $$1.6173$$
1200.m4 1200q1 $$[0, 1, 0, -1208, 21588]$$ $$-24389/12$$ $$-96000000000$$ $$$$ $$960$$ $$0.81260$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 1200.m have rank $$0$$.

## Complex multiplication

The elliptic curves in class 1200.m do not have complex multiplication.

## Modular form1200.2.a.m

sage: E.q_eigenform(10)

$$q + q^{3} - 2q^{7} + q^{9} - 2q^{11} + 6q^{13} + 2q^{17} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrrr} 1 & 5 & 2 & 10 \\ 5 & 1 & 10 & 2 \\ 2 & 10 & 1 & 5 \\ 10 & 2 & 5 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 