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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 3630c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3630.a3 | 3630c1 | \([1, 1, 0, -4872188, -3912956208]\) | \(7220044159551112609/448454983680000\) | \(794465359343124480000\) | \([2]\) | \(268800\) | \(2.7619\) | \(\Gamma_0(N)\)-optimal |
3630.a2 | 3630c2 | \([1, 1, 0, -14784508, 17059530448]\) | \(201738262891771037089/45727545600000000\) | \(81009136410681600000000\) | \([2, 2]\) | \(537600\) | \(3.1084\) | |
3630.a1 | 3630c3 | \([1, 1, 0, -221781628, 1271089482832]\) | \(680995599504466943307169/52207031250000000\) | \(92487940488281250000000\) | \([2]\) | \(1075200\) | \(3.4550\) | |
3630.a4 | 3630c4 | \([1, 1, 0, 33615492, 105466970448]\) | \(2371297246710590562911/4084000833203280000\) | \(-7235056600070435920080000\) | \([2]\) | \(1075200\) | \(3.4550\) |
Rank
sage: E.rank()
The elliptic curves in class 3630c have rank \(0\).
Complex multiplication
The elliptic curves in class 3630c do not have complex multiplication.Modular form 3630.2.a.c
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.