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SageMath
E = EllipticCurve("cd1")
E.isogeny_class()
Elliptic curves in class 246840cd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 246840.cd4 | 246840cd1 | \([0, 1, 0, -2448596, -44768747520]\) | \(-3579968623693264/1906997690433375\) | \(-864860860278231103584000\) | \([2]\) | \(38707200\) | \(3.2722\) | \(\Gamma_0(N)\)-optimal |
| 246840.cd3 | 246840cd2 | \([0, 1, 0, -204569416, -1114553823616]\) | \(521902963282042184836/6241849278890625\) | \(11323204352369412624000000\) | \([2, 2]\) | \(77414400\) | \(3.6187\) | |
| 246840.cd2 | 246840cd3 | \([0, 1, 0, -379414416, 1072687188384]\) | \(1664865424893526702418/826424127435466125\) | \(2998396423421341294328064000\) | \([2]\) | \(154828800\) | \(3.9653\) | |
| 246840.cd1 | 246840cd4 | \([0, 1, 0, -3263657536, -71764805772640]\) | \(1059623036730633329075378/154307373046875\) | \(559851364561500000000000\) | \([2]\) | \(154828800\) | \(3.9653\) |
Rank
sage: E.rank()
The elliptic curves in class 246840cd have rank \(1\).
Complex multiplication
The elliptic curves in class 246840cd do not have complex multiplication.Modular form 246840.2.a.cd
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.
