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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 61017.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 61017.a1 | 61017a4 | \([1, 0, 0, -270917, -54244602]\) | \(347873904937/395307\) | \(2498879062811043\) | \([2]\) | \(487872\) | \(1.8680\) | |
| 61017.a2 | 61017a2 | \([1, 0, 0, -21302, -377685]\) | \(169112377/88209\) | \(557601113189241\) | \([2, 2]\) | \(243936\) | \(1.5214\) | |
| 61017.a3 | 61017a1 | \([1, 0, 0, -12057, 504288]\) | \(30664297/297\) | \(1877444825553\) | \([2]\) | \(121968\) | \(1.1748\) | \(\Gamma_0(N)\)-optimal |
| 61017.a4 | 61017a3 | \([1, 0, 0, 80393, -2920060]\) | \(9090072503/5845851\) | \(-36953746501359699\) | \([2]\) | \(487872\) | \(1.8680\) |
Rank
sage: E.rank()
The elliptic curves in class 61017.a have rank \(0\).
Complex multiplication
The elliptic curves in class 61017.a do not have complex multiplication.Modular form 61017.2.a.a
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.
