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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 7440.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7440.b1 | 7440i4 | \([0, -1, 0, -10167536, 12482156736]\) | \(28379906689597370652529/1357352437500\) | \(5559715584000000\) | \([2]\) | \(207360\) | \(2.4985\) | |
| 7440.b2 | 7440i3 | \([0, -1, 0, -634416, 195871680]\) | \(-6894246873502147249/47925198774000\) | \(-196301614178304000\) | \([2]\) | \(103680\) | \(2.1519\) | |
| 7440.b3 | 7440i2 | \([0, -1, 0, -136496, 13993920]\) | \(68663623745397169/19216056254400\) | \(78708966418022400\) | \([2]\) | \(69120\) | \(1.9492\) | |
| 7440.b4 | 7440i1 | \([0, -1, 0, 22224, 1423296]\) | \(296354077829711/387386634240\) | \(-1586735653847040\) | \([2]\) | \(34560\) | \(1.6026\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7440.b have rank \(0\).
Complex multiplication
The elliptic curves in class 7440.b do not have complex multiplication.Modular form 7440.2.a.b
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
