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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 28314.bn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28314.bn1 | 28314bs2 | \([1, -1, 1, -30415793, -64572957237]\) | \(-2409558590804994721/674373039626\) | \(-870931179834146739594\) | \([]\) | \(2160000\) | \(2.9995\) | |
| 28314.bn2 | 28314bs1 | \([1, -1, 1, 304897, 9861063]\) | \(2427173723519/1437646496\) | \(-1856674400329086624\) | \([]\) | \(432000\) | \(2.1948\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 28314.bn have rank \(0\).
Complex multiplication
The elliptic curves in class 28314.bn do not have complex multiplication.Modular form 28314.2.a.bn
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
