# Properties

 Label 374790.dl Number of curves $6$ Conductor $374790$ CM no Rank $1$ Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("374790.dl1")

sage: E.isogeny_class()

## Elliptic curves in class 374790.dl

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
374790.dl1 374790dl5 [1, 0, 0, -8663435, 9814118535] [2] 14745600
374790.dl2 374790dl4 [1, 0, 0, -812065, -281511283] [2] 7372800
374790.dl3 374790dl3 [1, 0, 0, -542985, 152407125] [2, 2] 7372800
374790.dl4 374790dl6 [1, 0, 0, -110535, 388611315] [2] 14745600
374790.dl5 374790dl2 [1, 0, 0, -62485, -2217775] [2, 2] 3686400
374790.dl6 374790dl1 [1, 0, 0, 14395, -265023] [2] 1843200 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 374790.dl have rank $$1$$.

## Modular form 374790.2.a.dl

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.