Properties

 Label 2420g Number of curves 4 Conductor 2420 CM no Rank 0 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("2420.b1")

sage: E.isogeny_class()

Elliptic curves in class 2420g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2420.b4 2420g1 [0, 1, 0, -5485, -154992] [2] 4320 $$\Gamma_0(N)$$-optimal
2420.b3 2420g2 [0, 1, 0, -12140, 286900] [2] 8640
2420.b2 2420g3 [0, 1, 0, -53885, 4735828] [2] 12960
2420.b1 2420g4 [0, 1, 0, -859140, 306223300] [2] 25920

Rank

sage: E.rank()

The elliptic curves in class 2420g have rank $$0$$.

Modular form2420.2.a.b

sage: E.q_eigenform(10)

$$q - 2q^{3} + q^{5} + 4q^{7} + q^{9} + 4q^{13} - 2q^{15} + 4q^{19} + O(q^{20})$$

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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with Cremona labels.