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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 39270.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 39270.b1 | 39270a4 | \([1, 1, 0, -621078, 188135532]\) | \(26494958412646990069609/6077405565000\) | \(6077405565000\) | \([2]\) | \(368640\) | \(1.8337\) | |
| 39270.b2 | 39270a3 | \([1, 1, 0, -76358, -3625092]\) | \(49237527110356724329/22916114029642680\) | \(22916114029642680\) | \([2]\) | \(368640\) | \(1.8337\) | |
| 39270.b3 | 39270a2 | \([1, 1, 0, -38958, 2904948]\) | \(6539297416754410729/97931607681600\) | \(97931607681600\) | \([2, 2]\) | \(184320\) | \(1.4871\) | |
| 39270.b4 | 39270a1 | \([1, 1, 0, -238, 124852]\) | \(-1500730351849/6743874170880\) | \(-6743874170880\) | \([2]\) | \(92160\) | \(1.1406\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 39270.b have rank \(1\).
Complex multiplication
The elliptic curves in class 39270.b do not have complex multiplication.Modular form 39270.2.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.
