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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 104400ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 104400.dq2 | 104400ba1 | \([0, 0, 0, -2550, 46375]\) | \(10061824/725\) | \(132131250000\) | \([2]\) | \(73728\) | \(0.88060\) | \(\Gamma_0(N)\)-optimal |
| 104400.dq1 | 104400ba2 | \([0, 0, 0, -8175, -229250]\) | \(20720464/4205\) | \(12261780000000\) | \([2]\) | \(147456\) | \(1.2272\) |
Rank
sage: E.rank()
The elliptic curves in class 104400ba have rank \(1\).
Complex multiplication
The elliptic curves in class 104400ba do not have complex multiplication.Modular form 104400.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
