# Properties

 Label 1200.p Number of curves $2$ Conductor $1200$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("p1")

sage: E.isogeny_class()

## Elliptic curves in class 1200.p

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1200.p1 1200r1 $$[0, 1, 0, -133, 563]$$ $$-102400/3$$ $$-7680000$$ $$[]$$ $$240$$ $$0.10005$$ $$\Gamma_0(N)$$-optimal
1200.p2 1200r2 $$[0, 1, 0, 667, -29037]$$ $$20480/243$$ $$-388800000000$$ $$[]$$ $$1200$$ $$0.90477$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form1200.2.a.p

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 