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SageMath
E = EllipticCurve("co1")
E.isogeny_class()
Elliptic curves in class 98736.co
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 98736.co1 | 98736dl4 | \([0, 1, 0, -3071089424, 65505840040980]\) | \(441453577446719855661097/4354701912\) | \(31599083822795292672\) | \([2]\) | \(30965760\) | \(3.7734\) | |
| 98736.co2 | 98736dl2 | \([0, 1, 0, -191947664, 1023429527316]\) | \(107784459654566688937/10704361149504\) | \(77674204128773962727424\) | \([2, 2]\) | \(15482880\) | \(3.4269\) | |
| 98736.co3 | 98736dl3 | \([0, 1, 0, -177466384, 1184374473236]\) | \(-85183593440646799657/34223681512621656\) | \(-248337774363367561318465536\) | \([4]\) | \(30965760\) | \(3.7734\) | |
| 98736.co4 | 98736dl1 | \([0, 1, 0, -12906384, 13421858580]\) | \(32765849647039657/8229948198912\) | \(59719087149927389724672\) | \([2]\) | \(7741440\) | \(3.0803\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 98736.co have rank \(1\).
Complex multiplication
The elliptic curves in class 98736.co do not have complex multiplication.Modular form 98736.2.a.co
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
