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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 103455m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 103455.v3 | 103455m1 | \([1, -1, 0, -1069843605, -13468521751624]\) | \(104857852278310619039721/47155625\) | \(60899979245675625\) | \([2]\) | \(16957440\) | \(3.4641\) | \(\Gamma_0(N)\)-optimal |
| 103455.v2 | 103455m2 | \([1, -1, 0, -1069849050, -13468377795625]\) | \(104859453317683374662841/2223652969140625\) | \(2871776583816862644140625\) | \([2, 2]\) | \(33914880\) | \(3.8106\) | |
| 103455.v4 | 103455m3 | \([1, -1, 0, -1032501795, -14452321106404]\) | \(-94256762600623910012361/15323275604248046875\) | \(-19789519623045472869873046875\) | \([2]\) | \(67829760\) | \(4.1572\) | |
| 103455.v1 | 103455m4 | \([1, -1, 0, -1107283425, -12475221366250]\) | \(116256292809537371612841/15216540068579856875\) | \(19651674097575948472666936875\) | \([2]\) | \(67829760\) | \(4.1572\) |
Rank
sage: E.rank()
The elliptic curves in class 103455m have rank \(1\).
Complex multiplication
The elliptic curves in class 103455m do not have complex multiplication.Modular form 103455.2.a.m
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.
