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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 366597o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 366597.o4 | 366597o1 | \([1, -1, 0, -161973, 25123144]\) | \(4354703137/1617\) | \(174503669701977\) | \([2]\) | \(2027520\) | \(1.7001\) | \(\Gamma_0(N)\)-optimal |
| 366597.o3 | 366597o2 | \([1, -1, 0, -185778, 17272255]\) | \(6570725617/2614689\) | \(282172433908096809\) | \([2, 2]\) | \(4055040\) | \(2.0467\) | |
| 366597.o6 | 366597o3 | \([1, -1, 0, 599787, 124580434]\) | \(221115865823/190238433\) | \(-20530182236767892073\) | \([2]\) | \(8110080\) | \(2.3933\) | |
| 366597.o2 | 366597o4 | \([1, -1, 0, -1352223, -592778480]\) | \(2533811507137/58110129\) | \(6271138378079947449\) | \([2, 2]\) | \(8110080\) | \(2.3933\) | |
| 366597.o5 | 366597o5 | \([1, -1, 0, 147492, -1836642101]\) | \(3288008303/13504609503\) | \(-1457392650689976358743\) | \([2]\) | \(16220160\) | \(2.7398\) | |
| 366597.o1 | 366597o6 | \([1, -1, 0, -21515058, -38406159239]\) | \(10206027697760497/5557167\) | \(599719254574351527\) | \([2]\) | \(16220160\) | \(2.7398\) |
Rank
sage: E.rank()
The elliptic curves in class 366597o have rank \(1\).
Complex multiplication
The elliptic curves in class 366597o do not have complex multiplication.Modular form 366597.2.a.o
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
