Show commands:
SageMath
E = EllipticCurve("fa1")
E.isogeny_class()
Elliptic curves in class 101430fa
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 101430.eh4 | 101430fa1 | \([1, -1, 1, -1503438467, -19562707302141]\) | \(4381924769947287308715481/608122186185572352000\) | \(52156281003176326795886592000\) | \([2]\) | \(123863040\) | \(4.2368\) | \(\Gamma_0(N)\)-optimal |
| 101430.eh2 | 101430fa2 | \([1, -1, 1, -23188502147, -1359083786917629]\) | \(16077778198622525072705635801/388799208512064000000\) | \(33345799961949910983744000000\) | \([2, 2]\) | \(247726080\) | \(4.5834\) | |
| 101430.eh3 | 101430fa3 | \([1, -1, 1, -22324142147, -1465076104789629]\) | \(-14346048055032350809895395801/2509530875136386550792000\) | \(-215232728690183220417999317832000\) | \([2]\) | \(495452160\) | \(4.9300\) | |
| 101430.eh1 | 101430fa4 | \([1, -1, 1, -371013881027, -86982700785201021]\) | \(65853432878493908038433301506521/38511703125000000\) | \(3302999390134828125000000\) | \([2]\) | \(495452160\) | \(4.9300\) |
Rank
sage: E.rank()
The elliptic curves in class 101430fa have rank \(1\).
Complex multiplication
The elliptic curves in class 101430fa do not have complex multiplication.Modular form 101430.2.a.fa
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.
