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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 116380.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
116380.a1 | 116380e4 | \([0, 1, 0, -3756076, 2800628724]\) | \(154639330142416/33275\) | \(1261028916857600\) | \([2]\) | \(2566080\) | \(2.2822\) | |
116380.a2 | 116380e3 | \([0, 1, 0, -235581, 43377040]\) | \(610462990336/8857805\) | \(20980368604218320\) | \([2]\) | \(1283040\) | \(1.9356\) | |
116380.a3 | 116380e2 | \([0, 1, 0, -53076, 2641924]\) | \(436334416/171875\) | \(6513579116000000\) | \([2]\) | \(855360\) | \(1.7329\) | |
116380.a4 | 116380e1 | \([0, 1, 0, -23981, -1408100]\) | \(643956736/15125\) | \(35824685138000\) | \([2]\) | \(427680\) | \(1.3863\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 116380.a have rank \(0\).
Complex multiplication
The elliptic curves in class 116380.a do not have complex multiplication.Modular form 116380.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.