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SageMath
E = EllipticCurve("bot1")
E.isogeny_class()
Elliptic curves in class 705600.bot
sage: E.isogeny_class().curves
| LMFDB label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height |
|---|---|---|---|---|---|---|
| 705600.bot1 | \([0, 0, 0, -1249500, 394450000]\) | \(78608/21\) | \(57634833312000000000\) | \([2]\) | \(15728640\) | \(2.5000\) |
| 705600.bot2 | \([0, 0, 0, 3160500, 2555350000]\) | \(318028/441\) | \(-4841325998208000000000\) | \([2]\) | \(31457280\) | \(2.8466\) |
Rank
sage: E.rank()
The elliptic curves in class 705600.bot have rank \(0\).
Complex multiplication
The elliptic curves in class 705600.bot do not have complex multiplication.Modular form 705600.2.a.bot
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
