# Properties

 Label 97020cv Number of curves 4 Conductor 97020 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("97020.cu1")

sage: E.isogeny_class()

## Elliptic curves in class 97020cv

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
97020.cu4 97020cv1 [0, 0, 0, -19992, 1065701] [2] 248832 $$\Gamma_0(N)$$-optimal
97020.cu3 97020cv2 [0, 0, 0, -44247, -2024386] [2] 497664
97020.cu2 97020cv3 [0, 0, 0, -196392, -33076519] [2] 746496
97020.cu1 97020cv4 [0, 0, 0, -3131247, -2132671786] [2] 1492992

## Rank

sage: E.rank()

The elliptic curves in class 97020cv have rank $$0$$.

## Modular form 97020.2.a.cu

sage: E.q_eigenform(10)

$$q + q^{5} + q^{11} + 4q^{13} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.