# Properties

 Label 97104bj Number of curves $6$ Conductor $97104$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("97104.bb1")

sage: E.isogeny_class()

## Elliptic curves in class 97104bj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
97104.bb5 97104bj1 [0, -1, 0, -18592, -2148608] [2] 491520 $$\Gamma_0(N)$$-optimal
97104.bb4 97104bj2 [0, -1, 0, -388512, -93000960] [2, 2] 983040
97104.bb3 97104bj3 [0, -1, 0, -480992, -45281280] [2, 2] 1966080
97104.bb1 97104bj4 [0, -1, 0, -6214752, -5961189888] [2] 1966080
97104.bb6 97104bj5 [0, -1, 0, 1784768, -351612032] [2] 3932160
97104.bb2 97104bj6 [0, -1, 0, -4226432, 3313629312] [2] 3932160

## Rank

sage: E.rank()

The elliptic curves in class 97104bj have rank $$0$$.

## Modular form 97104.2.a.bb

sage: E.q_eigenform(10)

$$q - q^{3} + 2q^{5} - q^{7} + q^{9} - 4q^{11} + 6q^{13} - 2q^{15} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.