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SageMath
E = EllipticCurve("cb1")
E.isogeny_class()
Elliptic curves in class 247744cb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 247744.cb3 | 247744cb1 | \([0, 1, 0, -145889, -21495937]\) | \(11134383337/316\) | \(9745749508096\) | \([]\) | \(967680\) | \(1.5939\) | \(\Gamma_0(N)\)-optimal |
| 247744.cb2 | 247744cb2 | \([0, 1, 0, -255649, 14834623]\) | \(59914169497/31554496\) | \(973171562880434176\) | \([]\) | \(2903040\) | \(2.1432\) | |
| 247744.cb1 | 247744cb3 | \([0, 1, 0, -16359009, 25461859583]\) | \(15698803397448457/20709376\) | \(638697439762579456\) | \([]\) | \(8709120\) | \(2.6925\) |
Rank
sage: E.rank()
The elliptic curves in class 247744cb have rank \(1\).
Complex multiplication
The elliptic curves in class 247744cb do not have complex multiplication.Modular form 247744.2.a.cb
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
