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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 1176.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1176.a1 | 1176c3 | \([0, -1, 0, -7464, -245412]\) | \(381775972/567\) | \(68307950592\) | \([2]\) | \(1536\) | \(0.97991\) | |
1176.a2 | 1176c2 | \([0, -1, 0, -604, -1196]\) | \(810448/441\) | \(13282101504\) | \([2, 2]\) | \(768\) | \(0.63334\) | |
1176.a3 | 1176c1 | \([0, -1, 0, -359, 2724]\) | \(2725888/21\) | \(39530064\) | \([4]\) | \(384\) | \(0.28677\) | \(\Gamma_0(N)\)-optimal |
1176.a4 | 1176c4 | \([0, -1, 0, 2336, -11780]\) | \(11696828/7203\) | \(-867763964928\) | \([2]\) | \(1536\) | \(0.97991\) |
Rank
sage: E.rank()
The elliptic curves in class 1176.a have rank \(0\).
Complex multiplication
The elliptic curves in class 1176.a do not have complex multiplication.Modular form 1176.2.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.