# Properties

 Label 126350cu Number of curves $4$ Conductor $126350$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("126350.dh1")

sage: E.isogeny_class()

## Elliptic curves in class 126350cu

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
126350.dh4 126350cu1 [1, -1, 1, 20870, 1843497] [2] 691200 $$\Gamma_0(N)$$-optimal
126350.dh3 126350cu2 [1, -1, 1, -159630, 19893497] [2, 2] 1382400
126350.dh2 126350cu3 [1, -1, 1, -791380, -253022503] [2] 2764800
126350.dh1 126350cu4 [1, -1, 1, -2415880, 1445843497] [2] 2764800

## Rank

sage: E.rank()

The elliptic curves in class 126350cu have rank $$0$$.

## Modular form 126350.2.a.dh

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{7} + q^{8} - 3q^{9} + 4q^{11} - 6q^{13} + q^{14} + q^{16} - 2q^{17} - 3q^{18} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.