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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 78897l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 78897.g4 | 78897l1 | \([1, 0, 0, -475122, 126014163]\) | \(491411892194497/78897\) | \(1904381781393\) | \([2]\) | \(442368\) | \(1.7588\) | \(\Gamma_0(N)\)-optimal |
| 78897.g3 | 78897l2 | \([1, 0, 0, -476567, 125208720]\) | \(495909170514577/6224736609\) | \(150250009406563521\) | \([2, 2]\) | \(884736\) | \(2.1053\) | |
| 78897.g5 | 78897l3 | \([1, 0, 0, -82082, 326317173]\) | \(-2533811507137/1904381781393\) | \(-45967146650716453617\) | \([2]\) | \(1769472\) | \(2.4519\) | |
| 78897.g2 | 78897l4 | \([1, 0, 0, -894172, -127442305]\) | \(3275619238041697/1605271262049\) | \(38747345851424818881\) | \([2, 2]\) | \(1769472\) | \(2.4519\) | |
| 78897.g6 | 78897l5 | \([1, 0, 0, 3257313, -975175542]\) | \(158346567380527343/108665074944153\) | \(-2622910744354664184057\) | \([4]\) | \(3538944\) | \(2.7985\) | |
| 78897.g1 | 78897l6 | \([1, 0, 0, -11727337, -15447704248]\) | \(7389727131216686257/6115533215337\) | \(147614104956988695753\) | \([2]\) | \(3538944\) | \(2.7985\) |
Rank
sage: E.rank()
The elliptic curves in class 78897l have rank \(0\).
Complex multiplication
The elliptic curves in class 78897l do not have complex multiplication.Modular form 78897.2.a.l
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.
