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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 282897.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 282897.c1 | 282897c4 | \([1, -1, 1, -1509131, -713195558]\) | \(82483294977/17\) | \(78340652266257\) | \([2]\) | \(2580480\) | \(2.0533\) | |
| 282897.c2 | 282897c2 | \([1, -1, 1, -94646, -11045204]\) | \(20346417/289\) | \(1331791088526369\) | \([2, 2]\) | \(1290240\) | \(1.7067\) | |
| 282897.c3 | 282897c3 | \([1, -1, 1, -11441, -29849534]\) | \(-35937/83521\) | \(-384887624584120641\) | \([2]\) | \(2580480\) | \(2.0533\) | |
| 282897.c4 | 282897c1 | \([1, -1, 1, -11441, 204112]\) | \(35937/17\) | \(78340652266257\) | \([2]\) | \(645120\) | \(1.3601\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 282897.c have rank \(1\).
Complex multiplication
The elliptic curves in class 282897.c do not have complex multiplication.Modular form 282897.2.a.c
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
