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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 17424k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 17424.p2 | 17424k1 | \([0, 0, 0, -7986, 805255]\) | \(-2048/9\) | \(-247527916810416\) | \([2]\) | \(50688\) | \(1.4468\) | \(\Gamma_0(N)\)-optimal |
| 17424.p1 | 17424k2 | \([0, 0, 0, -187671, 31243894]\) | \(1661168/3\) | \(1320148889655552\) | \([2]\) | \(101376\) | \(1.7934\) |
Rank
sage: E.rank()
The elliptic curves in class 17424k have rank \(0\).
Complex multiplication
The elliptic curves in class 17424k do not have complex multiplication.Modular form 17424.2.a.k
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.
