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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 390.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
390.a1 | 390a3 | \([1, 1, 0, -483, -4293]\) | \(12501706118329/2570490\) | \(2570490\) | \([2]\) | \(128\) | \(0.22703\) | |
390.a2 | 390a2 | \([1, 1, 0, -33, -63]\) | \(4165509529/1368900\) | \(1368900\) | \([2, 2]\) | \(64\) | \(-0.11954\) | |
390.a3 | 390a1 | \([1, 1, 0, -13, 13]\) | \(273359449/9360\) | \(9360\) | \([2]\) | \(32\) | \(-0.46611\) | \(\Gamma_0(N)\)-optimal |
390.a4 | 390a4 | \([1, 1, 0, 97, -297]\) | \(99317171591/106616250\) | \(-106616250\) | \([2]\) | \(128\) | \(0.22703\) |
Rank
sage: E.rank()
The elliptic curves in class 390.a have rank \(1\).
Complex multiplication
The elliptic curves in class 390.a do not have complex multiplication.Modular form 390.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.