# Properties

 Label 235200.ce Number of curves $4$ Conductor $235200$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("ce1")

sage: E.isogeny_class()

## Elliptic curves in class 235200.ce

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
235200.ce1 235200ce3 [0, -1, 0, -29284033, 61004739937] [2] 14155776
235200.ce2 235200ce2 [0, -1, 0, -1844033, 938579937] [2, 2] 7077888
235200.ce3 235200ce1 [0, -1, 0, -276033, -35148063] [2] 3538944 $$\Gamma_0(N)$$-optimal
235200.ce4 235200ce4 [0, -1, 0, 507967, 3165923937] [2] 14155776

## Rank

sage: E.rank()

The elliptic curves in class 235200.ce have rank $$1$$.

## Complex multiplication

The elliptic curves in class 235200.ce do not have complex multiplication.

## Modular form 235200.2.a.ce

sage: E.q_eigenform(10)

$$q - q^{3} + q^{9} - 4q^{11} + 2q^{13} - 6q^{17} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.