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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 59177.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 59177.d1 | 59177b4 | \([1, -1, 0, -315683, 68348184]\) | \(82483294977/17\) | \(717069071897\) | \([2]\) | \(200448\) | \(1.6621\) | |
| 59177.d2 | 59177b2 | \([1, -1, 0, -19798, 1063935]\) | \(20346417/289\) | \(12190174222249\) | \([2, 2]\) | \(100224\) | \(1.3156\) | |
| 59177.d3 | 59177b1 | \([1, -1, 0, -2393, -18656]\) | \(35937/17\) | \(717069071897\) | \([2]\) | \(50112\) | \(0.96899\) | \(\Gamma_0(N)\)-optimal |
| 59177.d4 | 59177b3 | \([1, -1, 0, -2393, 2856650]\) | \(-35937/83521\) | \(-3522960350229961\) | \([2]\) | \(200448\) | \(1.6621\) |
Rank
sage: E.rank()
The elliptic curves in class 59177.d have rank \(1\).
Complex multiplication
The elliptic curves in class 59177.d do not have complex multiplication.Modular form 59177.2.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.
