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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 187200be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 187200.jp2 | 187200be1 | \([0, 0, 0, -8940, -282800]\) | \(3307949/468\) | \(11179524096000\) | \([2]\) | \(393216\) | \(1.2297\) | \(\Gamma_0(N)\)-optimal |
| 187200.jp1 | 187200be2 | \([0, 0, 0, -37740, 2539600]\) | \(248858189/27378\) | \(654002159616000\) | \([2]\) | \(786432\) | \(1.5763\) |
Rank
sage: E.rank()
The elliptic curves in class 187200be have rank \(1\).
Complex multiplication
The elliptic curves in class 187200be do not have complex multiplication.Modular form 187200.2.a.be
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.
