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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 31824bh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 31824.c2 | 31824bh1 | \([0, 0, 0, -20872947, 13099168690]\) | \(336811992790162430449/170089663019614208\) | \(507885012341959711260672\) | \([2]\) | \(6082560\) | \(3.2413\) | \(\Gamma_0(N)\)-optimal |
| 31824.c1 | 31824bh2 | \([0, 0, 0, -270073587, 1706915918770]\) | \(729596217166155478587889/697759680872204288\) | \(2083499242929508048699392\) | \([2]\) | \(12165120\) | \(3.5879\) |
Rank
sage: E.rank()
The elliptic curves in class 31824bh have rank \(0\).
Complex multiplication
The elliptic curves in class 31824bh do not have complex multiplication.Modular form 31824.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
