Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 248430.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
248430.j1 | 248430j1 | \([1, 1, 0, -2538, -19872]\) | \(1092727/540\) | \(894021562980\) | \([2]\) | \(442368\) | \(0.98634\) | \(\Gamma_0(N)\)-optimal |
248430.j2 | 248430j2 | \([1, 1, 0, 9292, -140538]\) | \(53582633/36450\) | \(-60346455501150\) | \([2]\) | \(884736\) | \(1.3329\) |
Rank
sage: E.rank()
The elliptic curves in class 248430.j have rank \(2\).
Complex multiplication
The elliptic curves in class 248430.j do not have complex multiplication.Modular form 248430.2.a.j
sage: E.q_eigenform(10)
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.