# Properties

 Label 97020.cu Number of curves $4$ Conductor $97020$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 97020.cu

sage: E.isogeny_class().curves

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

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 97020.cu do not have complex multiplication.

## 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 LMFDB 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 LMFDB labels. 