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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 792d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 792.b3 | 792d1 | \([0, 0, 0, -111, 434]\) | \(810448/33\) | \(6158592\) | \([4]\) | \(128\) | \(0.068572\) | \(\Gamma_0(N)\)-optimal |
| 792.b2 | 792d2 | \([0, 0, 0, -291, -1330]\) | \(3650692/1089\) | \(812934144\) | \([2, 2]\) | \(256\) | \(0.41515\) | |
| 792.b1 | 792d3 | \([0, 0, 0, -4251, -106666]\) | \(5690357426/891\) | \(1330255872\) | \([2]\) | \(512\) | \(0.76172\) | |
| 792.b4 | 792d4 | \([0, 0, 0, 789, -8890]\) | \(36382894/43923\) | \(-65576687616\) | \([2]\) | \(512\) | \(0.76172\) |
Rank
sage: E.rank()
The elliptic curves in class 792d have rank \(1\).
Complex multiplication
The elliptic curves in class 792d do not have complex multiplication.Modular form 792.2.a.d
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.
