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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 847a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 847.c1 | 847a1 | \([0, 1, 1, -10809, -436166]\) | \(-78843215872/539\) | \(-954871379\) | \([]\) | \(800\) | \(0.90395\) | \(\Gamma_0(N)\)-optimal |
| 847.c2 | 847a2 | \([0, 1, 1, -5969, -822761]\) | \(-13278380032/156590819\) | \(-277410187898459\) | \([]\) | \(2400\) | \(1.4533\) | |
| 847.c3 | 847a3 | \([0, 1, 1, 53321, 21262764]\) | \(9463555063808/115539436859\) | \(-204685160301366899\) | \([]\) | \(7200\) | \(2.0026\) |
Rank
sage: E.rank()
The elliptic curves in class 847a have rank \(0\).
Complex multiplication
The elliptic curves in class 847a do not have complex multiplication.Modular form 847.2.a.a
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
