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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 10200.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 10200.w1 | 10200bd4 | \([0, -1, 0, -674309408, 6739867696812]\) | \(1059623036730633329075378/154307373046875\) | \(4937835937500000000000\) | \([2]\) | \(2580480\) | \(3.5711\) | |
| 10200.w2 | 10200bd3 | \([0, -1, 0, -78391408, -100726467188]\) | \(1664865424893526702418/826424127435466125\) | \(26445572077934916000000000\) | \([2]\) | \(2580480\) | \(3.5711\) | |
| 10200.w3 | 10200bd2 | \([0, -1, 0, -42266408, 104680282812]\) | \(521902963282042184836/6241849278890625\) | \(99869588462250000000000\) | \([2, 2]\) | \(1290240\) | \(3.2245\) | |
| 10200.w4 | 10200bd1 | \([0, -1, 0, -505908, 4204519812]\) | \(-3579968623693264/1906997690433375\) | \(-7627990761733500000000\) | \([4]\) | \(645120\) | \(2.8779\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 10200.w have rank \(1\).
Complex multiplication
The elliptic curves in class 10200.w do not have complex multiplication.Modular form 10200.2.a.w
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.
