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SageMath
E = EllipticCurve("cv1")
E.isogeny_class()
Elliptic curves in class 51600.cv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 51600.cv1 | 51600db4 | \([0, 1, 0, -26549408, -52658476812]\) | \(32337636827233520089/3023437500000\) | \(193500000000000000000\) | \([2]\) | \(4423680\) | \(2.9304\) | |
| 51600.cv2 | 51600db3 | \([0, 1, 0, -9781408, 11192787188]\) | \(1617141066657115609/89723013444000\) | \(5742272860416000000000\) | \([4]\) | \(4423680\) | \(2.9304\) | |
| 51600.cv3 | 51600db2 | \([0, 1, 0, -1781408, -695212812]\) | \(9768641617435609/2396304000000\) | \(153363456000000000000\) | \([2, 2]\) | \(2211840\) | \(2.5839\) | |
| 51600.cv4 | 51600db1 | \([0, 1, 0, 266592, -68524812]\) | \(32740359775271/50724864000\) | \(-3246391296000000000\) | \([2]\) | \(1105920\) | \(2.2373\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 51600.cv have rank \(0\).
Complex multiplication
The elliptic curves in class 51600.cv do not have complex multiplication.Modular form 51600.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
