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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 28392.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28392.d1 | 28392q4 | \([0, -1, 0, -681464, 216754524]\) | \(7080974546692/189\) | \(934161306624\) | \([2]\) | \(184320\) | \(1.8107\) | |
| 28392.d2 | 28392q3 | \([0, -1, 0, -66304, -766052]\) | \(6522128932/3720087\) | \(18387096998280192\) | \([2]\) | \(184320\) | \(1.8107\) | |
| 28392.d3 | 28392q2 | \([0, -1, 0, -42644, 3388644]\) | \(6940769488/35721\) | \(44139121737984\) | \([2, 2]\) | \(92160\) | \(1.4641\) | |
| 28392.d4 | 28392q1 | \([0, -1, 0, -1239, 109368]\) | \(-2725888/64827\) | \(-5006520752688\) | \([2]\) | \(46080\) | \(1.1175\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 28392.d have rank \(2\).
Complex multiplication
The elliptic curves in class 28392.d do not have complex multiplication.Modular form 28392.2.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.
