Properties

 Label 2352.j Number of curves $2$ Conductor $2352$ CM no Rank $1$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("2352.j1")

sage: E.isogeny_class()

Elliptic curves in class 2352.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2352.j1 2352n2 [0, -1, 0, -2172, 36828] [2] 2688
2352.j2 2352n1 [0, -1, 0, -457, -2960] [2] 1344 $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 2352.j have rank $$1$$.

Modular form2352.2.a.j

sage: E.q_eigenform(10)

$$q - q^{3} + 2q^{5} + q^{9} - 2q^{11} - 4q^{13} - 2q^{15} + 6q^{17} - 8q^{19} + O(q^{20})$$

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.