# Properties

 Label 122034.g Number of curves 4 Conductor 122034 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("122034.g1")

sage: E.isogeny_class()

## Elliptic curves in class 122034.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
122034.g1 122034f3 [1, 1, 1, -148883, 21964625]  943488
122034.g2 122034f4 [1, 1, 1, -74923, 43886369]  1886976
122034.g3 122034f1 [1, 1, 1, -10208, -378691]  314496 $$\Gamma_0(N)$$-optimal
122034.g4 122034f2 [1, 1, 1, 8282, -1576843]  628992

## Rank

sage: E.rank()

The elliptic curves in class 122034.g have rank $$1$$.

## Modular form 122034.2.a.g

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} - q^{6} - 2q^{7} + q^{8} + q^{9} - q^{11} - q^{12} - 4q^{13} - 2q^{14} + q^{16} - 6q^{17} + q^{18} + 4q^{19} + O(q^{20})$$

## 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 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. 