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SageMath
E = EllipticCurve("eq1")
E.isogeny_class()
Elliptic curves in class 371280eq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 371280.eq3 | 371280eq1 | \([0, 1, 0, -1136296, 465747380]\) | \(39613077168432499369/8661219840000\) | \(35476356464640000\) | \([2]\) | \(4128768\) | \(2.1696\) | \(\Gamma_0(N)\)-optimal |
| 371280.eq2 | 371280eq2 | \([0, 1, 0, -1264296, 354182580]\) | \(54564527576482291369/18314631132033600\) | \(75016729116809625600\) | \([2, 2]\) | \(8257536\) | \(2.5162\) | |
| 371280.eq4 | 371280eq3 | \([0, 1, 0, 3686104, 2451172020]\) | \(1352279296967264534231/1415615917112986680\) | \(-5798362796494793441280\) | \([2]\) | \(16515072\) | \(2.8627\) | |
| 371280.eq1 | 371280eq4 | \([0, 1, 0, -8262696, -8880906060]\) | \(15231025329261085948969/501037266310733880\) | \(2052248642808765972480\) | \([2]\) | \(16515072\) | \(2.8627\) |
Rank
sage: E.rank()
The elliptic curves in class 371280eq have rank \(1\).
Complex multiplication
The elliptic curves in class 371280eq do not have complex multiplication.Modular form 371280.2.a.eq
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
