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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 350727.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 350727.c1 | 350727c5 | \([1, 1, 1, -10672057, 13412493314]\) | \(908031902324522977/161726530797\) | \(23941330761419773533\) | \([2]\) | \(12976128\) | \(2.7229\) | |
| 350727.c2 | 350727c3 | \([1, 1, 1, -734792, 164131616]\) | \(296380748763217/92608836489\) | \(13709431438904753721\) | \([2, 2]\) | \(6488064\) | \(2.3763\) | |
| 350727.c3 | 350727c2 | \([1, 1, 1, -287787, -57582864]\) | \(17806161424897/668584449\) | \(98974493279290161\) | \([2, 2]\) | \(3244032\) | \(2.0298\) | |
| 350727.c4 | 350727c1 | \([1, 1, 1, -285142, -58724446]\) | \(17319700013617/25857\) | \(3827763981873\) | \([2]\) | \(1622016\) | \(1.6832\) | \(\Gamma_0(N)\)-optimal |
| 350727.c5 | 350727c4 | \([1, 1, 1, 116898, -206183196]\) | \(1193377118543/124806800313\) | \(-18475885637580433257\) | \([2]\) | \(6488064\) | \(2.3763\) | |
| 350727.c6 | 350727c6 | \([1, 1, 1, 2050393, 1114436738]\) | \(6439735268725823/7345472585373\) | \(-1087393564300820451597\) | \([2]\) | \(12976128\) | \(2.7229\) |
Rank
sage: E.rank()
The elliptic curves in class 350727.c have rank \(1\).
Complex multiplication
The elliptic curves in class 350727.c do not have complex multiplication.Modular form 350727.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
