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SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 180336.bt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 180336.bt1 | 180336a1 | \([0, 1, 0, -865894960, 9806061542804]\) | \(147815204204011553/15178486401\) | \(7372736392123113542848512\) | \([2]\) | \(86900736\) | \(3.8045\) | \(\Gamma_0(N)\)-optimal |
| 180336.bt2 | 180336a2 | \([0, 1, 0, -799471200, 11373795126324]\) | \(-116340772335201233/47730591665289\) | \(-23184463911043192806656544768\) | \([2]\) | \(173801472\) | \(4.1511\) |
Rank
sage: E.rank()
The elliptic curves in class 180336.bt have rank \(1\).
Complex multiplication
The elliptic curves in class 180336.bt do not have complex multiplication.Modular form 180336.2.a.bt
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.
