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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 15210.ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15210.ba1 | 15210bf4 | \([1, -1, 1, -1819148, 896784581]\) | \(189208196468929/10860320250\) | \(38214684122149460250\) | \([2]\) | \(387072\) | \(2.5116\) | |
| 15210.ba2 | 15210bf2 | \([1, -1, 1, -313358, -67140043]\) | \(967068262369/4928040\) | \(17340510003958440\) | \([2]\) | \(129024\) | \(1.9623\) | |
| 15210.ba3 | 15210bf1 | \([1, -1, 1, -9158, -2162923]\) | \(-24137569/561600\) | \(-1976126496177600\) | \([2]\) | \(64512\) | \(1.6157\) | \(\Gamma_0(N)\)-optimal |
| 15210.ba4 | 15210bf3 | \([1, -1, 1, 82102, 57192581]\) | \(17394111071/411937500\) | \(-1449502508046937500\) | \([2]\) | \(193536\) | \(2.1650\) |
Rank
sage: E.rank()
The elliptic curves in class 15210.ba have rank \(1\).
Complex multiplication
The elliptic curves in class 15210.ba do not have complex multiplication.Modular form 15210.2.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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
