# Properties

 Label 38808cd Number of curves 4 Conductor 38808 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("38808.ca1")

sage: E.isogeny_class()

## Elliptic curves in class 38808cd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
38808.ca3 38808cd1 [0, 0, 0, -5439, -148862]  49152 $$\Gamma_0(N)$$-optimal
38808.ca2 38808cd2 [0, 0, 0, -14259, 456190] [2, 2] 98304
38808.ca4 38808cd3 [0, 0, 0, 38661, 3049270]  196608
38808.ca1 38808cd4 [0, 0, 0, -208299, 36586438]  196608

## Rank

sage: E.rank()

The elliptic curves in class 38808cd have rank $$0$$.

## Modular form 38808.2.a.ca

sage: E.q_eigenform(10)

$$q + 2q^{5} - q^{11} - 2q^{13} + 6q^{17} + O(q^{20})$$

## 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 Cremona 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 Cremona labels. 