Properties

 Label 342720gb Number of curves 4 Conductor 342720 CM no Rank 0 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("342720.gb1")

sage: E.isogeny_class()

Elliptic curves in class 342720gb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
342720.gb4 342720gb1 [0, 0, 0, 8052, -467728] [2] 1048576 $$\Gamma_0(N)$$-optimal
342720.gb3 342720gb2 [0, 0, 0, -63948, -5104528] [2, 2] 2097152
342720.gb2 342720gb3 [0, 0, 0, -308748, 61383152] [2] 4194304
342720.gb1 342720gb4 [0, 0, 0, -971148, -368347408] [2] 4194304

Rank

sage: E.rank()

The elliptic curves in class 342720gb have rank $$0$$.

Modular form 342720.2.a.gb

sage: E.q_eigenform(10)

$$q - q^{5} + q^{7} + 6q^{13} + q^{17} - 4q^{19} + O(q^{20})$$

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.