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SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 320790.ci
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 320790.ci1 | 320790ci3 | \([1, 0, 0, -98550451, 376553391905]\) | \(4385367890843575421521/24975000000\) | \(602835785775000000\) | \([2]\) | \(35389440\) | \(3.0234\) | |
| 320790.ci2 | 320790ci6 | \([1, 0, 0, -87603131, -314228388759]\) | \(3080272010107543650001/15465841417699560\) | \(373307814362780950769640\) | \([2]\) | \(70778880\) | \(3.3700\) | |
| 320790.ci3 | 320790ci4 | \([1, 0, 0, -8474931, 1065836961]\) | \(2788936974993502801/1593609593601600\) | \(38465861524620578510400\) | \([2, 2]\) | \(35389440\) | \(3.0234\) | |
| 320790.ci4 | 320790ci2 | \([1, 0, 0, -6162931, 5876184161]\) | \(1072487167529950801/2554882560000\) | \(61668654078896640000\) | \([2, 2]\) | \(17694720\) | \(2.6769\) | |
| 320790.ci5 | 320790ci1 | \([1, 0, 0, -244211, 159884385]\) | \(-66730743078481/419010969600\) | \(-10113906190476902400\) | \([2]\) | \(8847360\) | \(2.3303\) | \(\Gamma_0(N)\)-optimal |
| 320790.ci6 | 320790ci5 | \([1, 0, 0, 33661269, 8507089881]\) | \(174751791402194852399/102423900876336360\) | \(-2472263974651729356708840\) | \([2]\) | \(70778880\) | \(3.3700\) |
Rank
sage: E.rank()
The elliptic curves in class 320790.ci have rank \(1\).
Complex multiplication
The elliptic curves in class 320790.ci do not have complex multiplication.Modular form 320790.2.a.ci
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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
