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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 114950.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
114950.m1 | 114950m3 | \([1, 1, 0, -258700, 407282000]\) | \(-69173457625/2550136832\) | \(-70589421191168000000\) | \([]\) | \(2799360\) | \(2.4888\) | |
114950.m2 | 114950m1 | \([1, 1, 0, -46950, -3936500]\) | \(-413493625/152\) | \(-4207457375000\) | \([]\) | \(311040\) | \(1.3902\) | \(\Gamma_0(N)\)-optimal |
114950.m3 | 114950m2 | \([1, 1, 0, 28675, -14871875]\) | \(94196375/3511808\) | \(-97209095192000000\) | \([]\) | \(933120\) | \(1.9395\) |
Rank
sage: E.rank()
The elliptic curves in class 114950.m have rank \(0\).
Complex multiplication
The elliptic curves in class 114950.m do not have complex multiplication.Modular form 114950.2.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 LMFDB numbering.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.