# Properties

 Label 213444ce Number of curves 2 Conductor 213444 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("213444.dg1")

sage: E.isogeny_class()

## Elliptic curves in class 213444ce

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
213444.dg2 213444ce1 [0, 0, 0, 142296, 11413325]  2073600 $$\Gamma_0(N)$$-optimal
213444.dg1 213444ce2 [0, 0, 0, -658119, 97698062]  4147200

## Rank

sage: E.rank()

The elliptic curves in class 213444ce have rank $$1$$.

## Modular form 213444.2.a.dg

sage: E.q_eigenform(10)

$$q + 2q^{5} - 2q^{13} - 4q^{17} - 6q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 