Show commands:
SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 393008.ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 393008.ba1 | 393008ba3 | \([0, 0, 0, -103296611, 404044863266]\) | \(16798320881842096017/2132227789307\) | \(15472114051696632737792\) | \([2]\) | \(41287680\) | \(3.2796\) | |
| 393008.ba2 | 393008ba4 | \([0, 0, 0, -40976771, -96836758590]\) | \(1048626554636928177/48569076788309\) | \(352432464872134575509504\) | \([2]\) | \(41287680\) | \(3.2796\) | |
| 393008.ba3 | 393008ba2 | \([0, 0, 0, -7009651, 5166502770]\) | \(5249244962308257/1448621666569\) | \(10511653471226446680064\) | \([2, 2]\) | \(20643840\) | \(2.9330\) | |
| 393008.ba4 | 393008ba1 | \([0, 0, 0, 1131229, 527829346]\) | \(22062729659823/29354283343\) | \(-213003892954760900608\) | \([2]\) | \(10321920\) | \(2.5865\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 393008.ba have rank \(1\).
Complex multiplication
The elliptic curves in class 393008.ba do not have complex multiplication.Modular form 393008.2.a.ba
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.
