Show commands:
SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 28314.bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28314.bb1 | 28314v3 | \([1, -1, 0, -500418, -136128492]\) | \(-10730978619193/6656\) | \(-8596010801664\) | \([]\) | \(194400\) | \(1.8026\) | |
| 28314.bb2 | 28314v2 | \([1, -1, 0, -4923, -263763]\) | \(-10218313/17576\) | \(-22698841023144\) | \([]\) | \(64800\) | \(1.2533\) | |
| 28314.bb3 | 28314v1 | \([1, -1, 0, 522, 7398]\) | \(12167/26\) | \(-33578167194\) | \([]\) | \(21600\) | \(0.70403\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 28314.bb have rank \(1\).
Complex multiplication
The elliptic curves in class 28314.bb do not have complex multiplication.Modular form 28314.2.a.bb
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
