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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 41070.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 41070.w1 | 41070ba4 | \([1, 1, 1, -490537490565, -132238249729481205]\) | \(5087799435928552778197163696329/125914832087040\) | \(323063009970519114639360\) | \([2]\) | \(269660160\) | \(4.9566\) | |
| 41070.w2 | 41070ba2 | \([1, 1, 1, -30658629765, -2066227052243445]\) | \(1242142983306846366056931529/6179359141291622400\) | \(15854544939507477962135961600\) | \([2, 2]\) | \(134830080\) | \(4.6101\) | |
| 41070.w3 | 41070ba3 | \([1, 1, 1, -30139943045, -2139511469013493]\) | \(-1180159344892952613848670409/87759036144023189760000\) | \(-225165676663105825475650371840000\) | \([2]\) | \(269660160\) | \(4.9566\) | |
| 41070.w4 | 41070ba1 | \([1, 1, 1, -1948618885, -31135157021173]\) | \(318929057401476905525449/21353131537921474560\) | \(54786293501695912246813655040\) | \([4]\) | \(67415040\) | \(4.2635\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 41070.w have rank \(1\).
Complex multiplication
The elliptic curves in class 41070.w do not have complex multiplication.Modular form 41070.2.a.w
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.
