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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 43890e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 43890.f3 | 43890e1 | \([1, 1, 0, -26495826093, 1660012744259997]\) | \(2057103323961146379603477881442606169/6751241428377600000\) | \(6751241428377600000\) | \([2]\) | \(40140800\) | \(4.2013\) | \(\Gamma_0(N)\)-optimal |
| 43890.f2 | 43890e2 | \([1, 1, 0, -26495837613, 1660011228571293]\) | \(2057106007158172793619846312150133849/3726660700348180402500000000\) | \(3726660700348180402500000000\) | \([2, 2]\) | \(80281600\) | \(4.5478\) | |
| 43890.f4 | 43890e3 | \([1, 1, 0, -26225271933, 1695573245174637]\) | \(-1994728131675419567949045550395511129/87645898494930894470214843750000\) | \(-87645898494930894470214843750000\) | \([2]\) | \(160563200\) | \(4.8944\) | |
| 43890.f1 | 43890e4 | \([1, 1, 0, -26766587613, 1624352208121293]\) | \(2120814753125815346732459251938133849/87467018753661096920260194150000\) | \(87467018753661096920260194150000\) | \([2]\) | \(160563200\) | \(4.8944\) |
Rank
sage: E.rank()
The elliptic curves in class 43890e have rank \(0\).
Complex multiplication
The elliptic curves in class 43890e do not have complex multiplication.Modular form 43890.2.a.e
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 Cremona 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 Cremona labels.
