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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 32200c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 32200.l4 | 32200c1 | \([0, 0, 0, 550, 11625]\) | \(73598976/276115\) | \(-69028750000\) | \([4]\) | \(15360\) | \(0.76264\) | \(\Gamma_0(N)\)-optimal |
| 32200.l3 | 32200c2 | \([0, 0, 0, -5575, 140250]\) | \(4790692944/648025\) | \(2592100000000\) | \([2, 2]\) | \(30720\) | \(1.1092\) | |
| 32200.l2 | 32200c3 | \([0, 0, 0, -23075, -1207250]\) | \(84923690436/9794435\) | \(156710960000000\) | \([2]\) | \(61440\) | \(1.4558\) | |
| 32200.l1 | 32200c4 | \([0, 0, 0, -86075, 9719750]\) | \(4407931365156/100625\) | \(1610000000000\) | \([2]\) | \(61440\) | \(1.4558\) |
Rank
sage: E.rank()
The elliptic curves in class 32200c have rank \(0\).
Complex multiplication
The elliptic curves in class 32200c do not have complex multiplication.Modular form 32200.2.a.c
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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
