Show commands:
SageMath
E = EllipticCurve("oe1")
E.isogeny_class()
Elliptic curves in class 187200oe
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 187200.pd1 | 187200oe1 | \([0, 0, 0, -12110700, 16219694000]\) | \(65787589563409/10400000\) | \(31054233600000000000\) | \([2]\) | \(8847360\) | \(2.7507\) | \(\Gamma_0(N)\)-optimal |
| 187200.pd2 | 187200oe2 | \([0, 0, 0, -10958700, 19429166000]\) | \(-48743122863889/26406250000\) | \(-78848640000000000000000\) | \([2]\) | \(17694720\) | \(3.0973\) |
Rank
sage: E.rank()
The elliptic curves in class 187200oe have rank \(0\).
Complex multiplication
The elliptic curves in class 187200oe do not have complex multiplication.Modular form 187200.2.a.oe
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.
