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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 229320e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 229320.cy2 | 229320e1 | \([0, 0, 0, 317373, -72792146]\) | \(40254822716/49359375\) | \(-4334962819824000000\) | \([2]\) | \(2764800\) | \(2.2622\) | \(\Gamma_0(N)\)-optimal |
| 229320.cy1 | 229320e2 | \([0, 0, 0, -1887627, -699453146]\) | \(4234737878642/1247410125\) | \(219106360765184256000\) | \([2]\) | \(5529600\) | \(2.6088\) |
Rank
sage: E.rank()
The elliptic curves in class 229320e have rank \(0\).
Complex multiplication
The elliptic curves in class 229320e do not have complex multiplication.Modular form 229320.2.a.e
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
