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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 1449.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1449.d1 | 1449e3 | \([1, -1, 0, -1113, -14014]\) | \(209267191953/55223\) | \(40257567\) | \([2]\) | \(640\) | \(0.44367\) | |
| 1449.d2 | 1449e2 | \([1, -1, 0, -78, -145]\) | \(72511713/25921\) | \(18896409\) | \([2, 2]\) | \(320\) | \(0.097099\) | |
| 1449.d3 | 1449e1 | \([1, -1, 0, -33, 80]\) | \(5545233/161\) | \(117369\) | \([2]\) | \(160\) | \(-0.24948\) | \(\Gamma_0(N)\)-optimal |
| 1449.d4 | 1449e4 | \([1, -1, 0, 237, -1216]\) | \(2014698447/1958887\) | \(-1428028623\) | \([2]\) | \(640\) | \(0.44367\) |
Rank
sage: E.rank()
The elliptic curves in class 1449.d have rank \(0\).
Complex multiplication
The elliptic curves in class 1449.d do not have complex multiplication.Modular form 1449.2.a.d
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.
