Properties

 Label 2394.b Number of curves $4$ Conductor $2394$ CM no Rank $1$ Graph Related objects

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

sage: E.isogeny_class()

Elliptic curves in class 2394.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2394.b1 2394f4 $$[1, -1, 0, -10953, 443961]$$ $$199350693197713/547428$$ $$399075012$$ $$$$ $$2048$$ $$0.88357$$
2394.b2 2394f3 $$[1, -1, 0, -1953, -24111]$$ $$1130389181713/295568028$$ $$215469092412$$ $$$$ $$2048$$ $$0.88357$$
2394.b3 2394f2 $$[1, -1, 0, -693, 6885]$$ $$50529889873/2547216$$ $$1856920464$$ $$[2, 2]$$ $$1024$$ $$0.53699$$
2394.b4 2394f1 $$[1, -1, 0, 27, 405]$$ $$2924207/102144$$ $$-74462976$$ $$$$ $$512$$ $$0.19042$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 2394.b have rank $$1$$.

Complex multiplication

The elliptic curves in class 2394.b do not have complex multiplication.

Modular form2394.2.a.b

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - 2 q^{5} - q^{7} - q^{8} + 2 q^{10} + 2 q^{13} + q^{14} + q^{16} + 2 q^{17} + q^{19} + O(q^{20})$$ 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels. 