# Properties

 Label 53958bh Number of curves 6 Conductor 53958 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("53958.bn1")

sage: E.isogeny_class()

## Elliptic curves in class 53958bh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
53958.bn5 53958bh1 [1, 0, 0, -17997, -863343] [2] 202752 $$\Gamma_0(N)$$-optimal
53958.bn4 53958bh2 [1, 0, 0, -60317, 4697505] [2, 2] 405504
53958.bn6 53958bh3 [1, 0, 0, 119543, 27395837] [2] 811008
53958.bn2 53958bh4 [1, 0, 0, -917297, 338062725] [2, 2] 811008
53958.bn3 53958bh5 [1, 0, 0, -869687, 374731947] [2] 1622016
53958.bn1 53958bh6 [1, 0, 0, -14676587, 21640195503] [2] 1622016

## Rank

sage: E.rank()

The elliptic curves in class 53958bh have rank $$0$$.

## Modular form 53958.2.a.bn

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + 2q^{5} + q^{6} + q^{8} + q^{9} + 2q^{10} + 4q^{11} + q^{12} - 2q^{13} + 2q^{15} + q^{16} - q^{17} + q^{18} - 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.