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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 47096d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 47096.h4 | 47096d1 | \([0, 0, 0, -21866, 121945]\) | \(121485312/69629\) | \(662671248286544\) | \([4]\) | \(147840\) | \(1.5336\) | \(\Gamma_0(N)\)-optimal |
| 47096.h2 | 47096d2 | \([0, 0, 0, -227911, -41705190]\) | \(8597884752/41209\) | \(6275091004182784\) | \([2, 2]\) | \(295680\) | \(1.8802\) | |
| 47096.h3 | 47096d3 | \([0, 0, 0, -110171, -84727386]\) | \(-242793828/4950967\) | \(-3015629448295840768\) | \([2]\) | \(591360\) | \(2.2268\) | |
| 47096.h1 | 47096d4 | \([0, 0, 0, -3642371, -2675619634]\) | \(8773811642628/203\) | \(123647113382912\) | \([2]\) | \(591360\) | \(2.2268\) |
Rank
sage: E.rank()
The elliptic curves in class 47096d have rank \(0\).
Complex multiplication
The elliptic curves in class 47096d do not have complex multiplication.Modular form 47096.2.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.
