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SageMath
E = EllipticCurve("cj1")
E.isogeny_class()
Elliptic curves in class 94864cj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 94864.cd1 | 94864cj1 | \([0, 1, 0, -8474517, -9498440701]\) | \(-78843215872/539\) | \(-460143259107209216\) | \([]\) | \(2764800\) | \(2.5700\) | \(\Gamma_0(N)\)-optimal |
| 94864.cd2 | 94864cj2 | \([0, 1, 0, -4679957, -18019125181]\) | \(-13278380032/156590819\) | \(-133681279779085528641536\) | \([]\) | \(8294400\) | \(3.1194\) | |
| 94864.cd3 | 94864cj3 | \([0, 1, 0, 41803403, 466383969379]\) | \(9463555063808/115539436859\) | \(-98635794121914426574647296\) | \([]\) | \(24883200\) | \(3.6687\) |
Rank
sage: E.rank()
The elliptic curves in class 94864cj have rank \(0\).
Complex multiplication
The elliptic curves in class 94864cj do not have complex multiplication.Modular form 94864.2.a.cj
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.
