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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 370.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
370.a1 | 370c3 | \([1, 0, 1, -54, 146]\) | \(-16954786009/370\) | \(-370\) | \([3]\) | \(324\) | \(-0.39121\) | |
370.a2 | 370c1 | \([1, 0, 1, -19, 342]\) | \(-702595369/50653000\) | \(-50653000\) | \([3]\) | \(108\) | \(0.15809\) | \(\Gamma_0(N)\)-optimal |
370.a3 | 370c2 | \([1, 0, 1, 166, -9204]\) | \(510273943271/37000000000\) | \(-37000000000\) | \([]\) | \(324\) | \(0.70740\) |
Rank
sage: E.rank()
The elliptic curves in class 370.a have rank \(0\).
Complex multiplication
The elliptic curves in class 370.a do not have complex multiplication.Modular form 370.2.a.a
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.