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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 4624.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4624.d1 | 4624e3 | \([0, 0, 0, -419339, 104519162]\) | \(82483294977/17\) | \(1680747204608\) | \([4]\) | \(18432\) | \(1.7331\) | |
| 4624.d2 | 4624e2 | \([0, 0, 0, -26299, 1621290]\) | \(20346417/289\) | \(28572702478336\) | \([2, 2]\) | \(9216\) | \(1.3865\) | |
| 4624.d3 | 4624e1 | \([0, 0, 0, -3179, -29478]\) | \(35937/17\) | \(1680747204608\) | \([2]\) | \(4608\) | \(1.0400\) | \(\Gamma_0(N)\)-optimal |
| 4624.d4 | 4624e4 | \([0, 0, 0, -3179, 4372570]\) | \(-35937/83521\) | \(-8257511016239104\) | \([2]\) | \(18432\) | \(1.7331\) |
Rank
sage: E.rank()
The elliptic curves in class 4624.d have rank \(0\).
Complex multiplication
The elliptic curves in class 4624.d do not have complex multiplication.Modular form 4624.2.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 LMFDB 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 LMFDB labels.
