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SageMath
E = EllipticCurve("di1")
E.isogeny_class()
Elliptic curves in class 189630.di
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 189630.di1 | 189630bg3 | \([1, -1, 1, -369788, 86054217]\) | \(65202655558249/512820150\) | \(43982595036138150\) | \([2]\) | \(1769472\) | \(2.0218\) | |
| 189630.di2 | 189630bg2 | \([1, -1, 1, -39038, -734583]\) | \(76711450249/41602500\) | \(3568085048902500\) | \([2, 2]\) | \(884736\) | \(1.6752\) | |
| 189630.di3 | 189630bg1 | \([1, -1, 1, -30218, -2011719]\) | \(35578826569/51600\) | \(4425531843600\) | \([2]\) | \(442368\) | \(1.3286\) | \(\Gamma_0(N)\)-optimal |
| 189630.di4 | 189630bg4 | \([1, -1, 1, 150592, -5892519]\) | \(4403686064471/2721093750\) | \(-233377655814843750\) | \([2]\) | \(1769472\) | \(2.0218\) |
Rank
sage: E.rank()
The elliptic curves in class 189630.di have rank \(0\).
Complex multiplication
The elliptic curves in class 189630.di do not have complex multiplication.Modular form 189630.2.a.di
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.
