# Properties

 Label 374850ir Number of curves $6$ Conductor $374850$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("374850.ir1")

sage: E.isogeny_class()

## Elliptic curves in class 374850ir

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
374850.ir5 374850ir1 [1, -1, 1, -774440330, 8285076708297] [2] 188743680 $$\Gamma_0(N)$$-optimal
374850.ir4 374850ir2 [1, -1, 1, -1000232330, 3060249828297] [2, 2] 377487360
374850.ir6 374850ir3 [1, -1, 1, 3857823670, 24066483972297] [2] 754974720
374850.ir2 374850ir4 [1, -1, 1, -9470960330, -352337614139703] [2, 2] 754974720
374850.ir3 374850ir5 [1, -1, 1, -3225959330, -810046227431703] [2] 1509949440
374850.ir1 374850ir6 [1, -1, 1, -151247609330, -22640193943535703] [2] 1509949440

## Rank

sage: E.rank()

The elliptic curves in class 374850ir have rank $$0$$.

## Modular form 374850.2.a.ir

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{8} - 4q^{11} - 2q^{13} + q^{16} - q^{17} - 4q^{19} + O(q^{20})$$

## 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.