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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 67600.bh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 67600.bh1 | 67600da2 | \([0, -1, 0, -339408, 76222912]\) | \(-349938025/8\) | \(-98853048320000\) | \([]\) | \(311040\) | \(1.7988\) | |
| 67600.bh2 | 67600da3 | \([0, -1, 0, -204208, -42753088]\) | \(-121945/32\) | \(-247132620800000000\) | \([]\) | \(518400\) | \(2.0542\) | |
| 67600.bh3 | 67600da1 | \([0, -1, 0, -1408, 240512]\) | \(-25/2\) | \(-24713262080000\) | \([]\) | \(103680\) | \(1.2495\) | \(\Gamma_0(N)\)-optimal |
| 67600.bh4 | 67600da4 | \([0, -1, 0, 1485792, 315526912]\) | \(46969655/32768\) | \(-253063803699200000000\) | \([]\) | \(1555200\) | \(2.6035\) |
Rank
sage: E.rank()
The elliptic curves in class 67600.bh have rank \(1\).
Complex multiplication
The elliptic curves in class 67600.bh do not have complex multiplication.Modular form 67600.2.a.bh
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.
\(\left(\begin{array}{rrrr} 1 & 15 & 3 & 5 \\ 15 & 1 & 5 & 3 \\ 3 & 5 & 1 & 15 \\ 5 & 3 & 15 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
