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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 19152bh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 19152.o3 | 19152bh1 | \([0, 0, 0, -270555, 38607242]\) | \(19804628171203875/5638671302656\) | \(623591936703332352\) | \([2]\) | \(221184\) | \(2.1212\) | \(\Gamma_0(N)\)-optimal |
| 19152.o4 | 19152bh2 | \([0, 0, 0, 712485, 254679434]\) | \(361682234074684125/462672528510976\) | \(-51167880273085857792\) | \([2]\) | \(442368\) | \(2.4678\) | |
| 19152.o1 | 19152bh3 | \([0, 0, 0, -20115675, 34725620106]\) | \(11165451838341046875/572244736\) | \(46135267896066048\) | \([2]\) | \(663552\) | \(2.6705\) | |
| 19152.o2 | 19152bh4 | \([0, 0, 0, -20081115, 34850886282]\) | \(-11108001800138902875/79947274872976\) | \(-6445474657586325946368\) | \([2]\) | \(1327104\) | \(3.0171\) |
Rank
sage: E.rank()
The elliptic curves in class 19152bh have rank \(0\).
Complex multiplication
The elliptic curves in class 19152bh do not have complex multiplication.Modular form 19152.2.a.bh
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
