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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 95304.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
95304.d1 | 95304n4 | \([0, -1, 0, -254264, -49263972]\) | \(37736227588/33\) | \(1589774410752\) | \([2]\) | \(580608\) | \(1.6415\) | |
95304.d2 | 95304n3 | \([0, -1, 0, -37664, 1749660]\) | \(122657188/43923\) | \(2115989740710912\) | \([2]\) | \(580608\) | \(1.6415\) | |
95304.d3 | 95304n2 | \([0, -1, 0, -16004, -754236]\) | \(37642192/1089\) | \(13115638888704\) | \([2, 2]\) | \(290304\) | \(1.2950\) | |
95304.d4 | 95304n1 | \([0, -1, 0, 241, -39456]\) | \(2048/891\) | \(-670686079536\) | \([2]\) | \(145152\) | \(0.94839\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 95304.d have rank \(1\).
Complex multiplication
The elliptic curves in class 95304.d do not have complex multiplication.Modular form 95304.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.