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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 101695.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 101695.b1 | 101695a4 | \([1, -1, 1, -109438, -13903758]\) | \(22930509321/6875\) | \(43459370961875\) | \([2]\) | \(322560\) | \(1.5949\) | |
| 101695.b2 | 101695a3 | \([1, -1, 1, -53968, 4726766]\) | \(2749884201/73205\) | \(462755382002045\) | \([2]\) | \(322560\) | \(1.5949\) | |
| 101695.b3 | 101695a2 | \([1, -1, 1, -7743, -154594]\) | \(8120601/3025\) | \(19122123223225\) | \([2, 2]\) | \(161280\) | \(1.2484\) | |
| 101695.b4 | 101695a1 | \([1, -1, 1, 1502, -17768]\) | \(59319/55\) | \(-347674967695\) | \([2]\) | \(80640\) | \(0.90179\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 101695.b have rank \(0\).
Complex multiplication
The elliptic curves in class 101695.b do not have complex multiplication.Modular form 101695.2.a.b
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
