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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 277200ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 277200.ba3 | 277200ba1 | \([0, 0, 0, -1803675, -809581750]\) | \(13908844989649/1980372240\) | \(92396247229440000000\) | \([2]\) | \(7077888\) | \(2.5568\) | \(\Gamma_0(N)\)-optimal |
| 277200.ba2 | 277200ba2 | \([0, 0, 0, -7635675, 7314394250]\) | \(1055257664218129/115307784900\) | \(5379800012294400000000\) | \([2, 2]\) | \(14155776\) | \(2.9034\) | |
| 277200.ba1 | 277200ba3 | \([0, 0, 0, -118767675, 498184438250]\) | \(3971101377248209009/56495958750\) | \(2635875451440000000000\) | \([2]\) | \(28311552\) | \(3.2500\) | |
| 277200.ba4 | 277200ba4 | \([0, 0, 0, 10184325, 36378814250]\) | \(2503876820718671/13702874328990\) | \(-639321304693357440000000\) | \([2]\) | \(28311552\) | \(3.2500\) |
Rank
sage: E.rank()
The elliptic curves in class 277200ba have rank \(1\).
Complex multiplication
The elliptic curves in class 277200ba do not have complex multiplication.Modular form 277200.2.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 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.
