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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 39270m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
39270.m3 | 39270m1 | \([1, 1, 0, -357, -2499]\) | \(5053913144281/538784400\) | \(538784400\) | \([2]\) | \(24576\) | \(0.40979\) | \(\Gamma_0(N)\)-optimal |
39270.m2 | 39270m2 | \([1, 1, 0, -1337, 15729]\) | \(264621653112601/38553322500\) | \(38553322500\) | \([2, 2]\) | \(49152\) | \(0.75636\) | |
39270.m4 | 39270m3 | \([1, 1, 0, 2233, 89271]\) | \(1230512292220679/4083466406250\) | \(-4083466406250\) | \([2]\) | \(98304\) | \(1.1029\) | |
39270.m1 | 39270m4 | \([1, 1, 0, -20587, 1128379]\) | \(965019006588684601/26046023850\) | \(26046023850\) | \([2]\) | \(98304\) | \(1.1029\) |
Rank
sage: E.rank()
The elliptic curves in class 39270m have rank \(2\).
Complex multiplication
The elliptic curves in class 39270m do not have complex multiplication.Modular form 39270.2.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.