# Properties

 Label 6762bh Number of curves $6$ Conductor $6762$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("6762.bl1")

sage: E.isogeny_class()

## Elliptic curves in class 6762bh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6762.bl5 6762bh1 [1, 0, 0, 6173, -381823] [2] 24576 $$\Gamma_0(N)$$-optimal
6762.bl4 6762bh2 [1, 0, 0, -56547, -4433535] [2, 2] 49152
6762.bl2 6762bh3 [1, 0, 0, -867987, -311320143] [2] 98304
6762.bl3 6762bh4 [1, 0, 0, -248627, 43394385] [2, 2] 98304
6762.bl1 6762bh5 [1, 0, 0, -3877567, 2938562717] [4] 196608
6762.bl6 6762bh6 [1, 0, 0, 307033, 209981253] [2] 196608

## Rank

sage: E.rank()

The elliptic curves in class 6762bh have rank $$0$$.

## Modular form6762.2.a.bl

sage: E.q_eigenform(10)

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

## 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.