Properties

 Label 46410k Number of curves 4 Conductor 46410 CM no Rank 0 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("46410.i1")

sage: E.isogeny_class()

Elliptic curves in class 46410k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
46410.i4 46410k1 [1, 1, 0, -773, -43827] [2] 90112 $$\Gamma_0(N)$$-optimal
46410.i3 46410k2 [1, 1, 0, -23893, -1426403] [2, 2] 180224
46410.i2 46410k3 [1, 1, 0, -35793, 127737] [2] 360448
46410.i1 46410k4 [1, 1, 0, -381913, -91003007] [2] 360448

Rank

sage: E.rank()

The elliptic curves in class 46410k have rank $$0$$.

Modular form 46410.2.a.i

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} + q^{7} - q^{8} + q^{9} + q^{10} - 4q^{11} - q^{12} + q^{13} - q^{14} + q^{15} + q^{16} + q^{17} - q^{18} + 4q^{19} + O(q^{20})$$

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.