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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 630h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 630.j3 | 630h1 | \([1, -1, 1, -47, 119]\) | \(416832723/56000\) | \(1512000\) | \([6]\) | \(96\) | \(-0.086795\) | \(\Gamma_0(N)\)-optimal |
| 630.j4 | 630h2 | \([1, -1, 1, 73, 551]\) | \(1613964717/6125000\) | \(-165375000\) | \([6]\) | \(192\) | \(0.25978\) | |
| 630.j1 | 630h3 | \([1, -1, 1, -947, -10961]\) | \(4767078987/6860\) | \(135025380\) | \([2]\) | \(288\) | \(0.46251\) | |
| 630.j2 | 630h4 | \([1, -1, 1, -677, -17549]\) | \(-1740992427/5882450\) | \(-115784263350\) | \([2]\) | \(576\) | \(0.80908\) |
Rank
sage: E.rank()
The elliptic curves in class 630h have rank \(0\).
Complex multiplication
The elliptic curves in class 630h do not have complex multiplication.Modular form 630.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
