# Properties

 Label 11200c Number of curves $3$ Conductor $11200$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 11200c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11200.cg2 11200c1 $$[0, 1, 0, -133, 613]$$ $$-262144/35$$ $$-35000000$$ $$[]$$ $$2304$$ $$0.18014$$ $$\Gamma_0(N)$$-optimal
11200.cg3 11200c2 $$[0, 1, 0, 867, -1387]$$ $$71991296/42875$$ $$-42875000000$$ $$[]$$ $$6912$$ $$0.72945$$
11200.cg1 11200c3 $$[0, 1, 0, -13133, -610387]$$ $$-250523582464/13671875$$ $$-13671875000000$$ $$[]$$ $$20736$$ $$1.2788$$

## Rank

sage: E.rank()

The elliptic curves in class 11200c have rank $$1$$.

## Complex multiplication

The elliptic curves in class 11200c do not have complex multiplication.

## Modular form 11200.2.a.c

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 