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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 139230.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
139230.m1 | 139230dl2 | \([1, -1, 0, -1629967680, 15279462590976]\) | \(656951279855452335833136583681/241839679711912280107200000\) | \(176301126509984052198148800000\) | \([2]\) | \(162570240\) | \(4.3120\) | |
139230.m2 | 139230dl1 | \([1, -1, 0, 314032320, 1692068990976]\) | \(4698067216568883444047416319/4415596696143360000000000\) | \(-3218969991488509440000000000\) | \([2]\) | \(81285120\) | \(3.9654\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 139230.m have rank \(0\).
Complex multiplication
The elliptic curves in class 139230.m do not have complex multiplication.Modular form 139230.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.