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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 6050.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6050.h1 | 6050g4 | \([1, 1, 0, -379700, 89899000]\) | \(-349938025/8\) | \(-138403203125000\) | \([]\) | \(40500\) | \(1.8269\) | |
| 6050.h2 | 6050g3 | \([1, 1, 0, -1575, 283375]\) | \(-25/2\) | \(-34600800781250\) | \([]\) | \(13500\) | \(1.2776\) | |
| 6050.h3 | 6050g1 | \([1, 1, 0, -365, -3395]\) | \(-121945/32\) | \(-1417248800\) | \([]\) | \(2700\) | \(0.47285\) | \(\Gamma_0(N)\)-optimal |
| 6050.h4 | 6050g2 | \([1, 1, 0, 2660, 25040]\) | \(46969655/32768\) | \(-1451262771200\) | \([]\) | \(8100\) | \(1.0222\) |
Rank
sage: E.rank()
The elliptic curves in class 6050.h have rank \(0\).
Complex multiplication
The elliptic curves in class 6050.h do not have complex multiplication.Modular form 6050.2.a.h
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 15 & 5 \\ 3 & 1 & 5 & 15 \\ 15 & 5 & 1 & 3 \\ 5 & 15 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
