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SageMath
E = EllipticCurve("cv1")
E.isogeny_class()
Elliptic curves in class 54150.cv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
54150.cv1 | 54150cr3 | \([1, 0, 0, -3862888, 2921896892]\) | \(8671983378625/82308\) | \(60503943333562500\) | \([2]\) | \(1866240\) | \(2.3824\) | |
54150.cv2 | 54150cr4 | \([1, 0, 0, -3772638, 3064943142]\) | \(-8078253774625/846825858\) | \(-622494820987357781250\) | \([2]\) | \(3732480\) | \(2.7290\) | |
54150.cv3 | 54150cr1 | \([1, 0, 0, -72388, -578608]\) | \(57066625/32832\) | \(24134536953000000\) | \([2]\) | \(622080\) | \(1.8331\) | \(\Gamma_0(N)\)-optimal |
54150.cv4 | 54150cr2 | \([1, 0, 0, 288612, -4549608]\) | \(3616805375/2105352\) | \(-1547627182111125000\) | \([2]\) | \(1244160\) | \(2.1797\) |
Rank
sage: E.rank()
The elliptic curves in class 54150.cv have rank \(0\).
Complex multiplication
The elliptic curves in class 54150.cv do not have complex multiplication.Modular form 54150.2.a.cv
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.