Properties

 Label 1848b Number of curves 4 Conductor 1848 CM no Rank 1 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("1848.d1")

sage: E.isogeny_class()

Elliptic curves in class 1848b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1848.d3 1848b1 [0, -1, 0, -586972, -172895372] [2] 11520 $$\Gamma_0(N)$$-optimal
1848.d2 1848b2 [0, -1, 0, -586992, -172882980] [2, 2] 23040
1848.d1 1848b3 [0, -1, 0, -640232, -139597332] [2] 46080
1848.d4 1848b4 [0, -1, 0, -534072, -205375860] [2] 46080

Rank

sage: E.rank()

The elliptic curves in class 1848b have rank $$1$$.

Modular form1848.2.a.d

sage: E.q_eigenform(10)

$$q - q^{3} + 2q^{5} + q^{7} + q^{9} + q^{11} - 6q^{13} - 2q^{15} - 2q^{17} - 8q^{19} + O(q^{20})$$

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.