# Properties

 Label 22308.c Number of curves 2 Conductor 22308 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("22308.c1")

sage: E.isogeny_class()

## Elliptic curves in class 22308.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
22308.c1 22308e2 [0, 1, 0, -2084, -18108]  27648
22308.c2 22308e1 [0, 1, 0, 451, -1884]  13824 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 22308.c have rank $$1$$.

## Modular form 22308.2.a.c

sage: E.q_eigenform(10)

$$q + q^{3} - 2q^{5} + 2q^{7} + q^{9} - q^{11} - 2q^{15} + 4q^{17} + 6q^{19} + O(q^{20})$$

## 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 LMFDB 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 LMFDB labels. 