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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 126960g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 126960.bj4 | 126960g1 | \([0, -1, 0, -2092900, -7458662048]\) | \(-26752376766544/618796614375\) | \(-23450651371313485920000\) | \([2]\) | \(6488064\) | \(2.9732\) | \(\Gamma_0(N)\)-optimal |
| 126960.bj3 | 126960g2 | \([0, -1, 0, -71508280, -231698105600]\) | \(266763091319403556/1355769140625\) | \(205519349771456400000000\) | \([2, 2]\) | \(12976128\) | \(3.3197\) | |
| 126960.bj2 | 126960g3 | \([0, -1, 0, -110929360, 52228280992]\) | \(497927680189263938/284271240234375\) | \(86184644127187500000000000\) | \([4]\) | \(25952256\) | \(3.6663\) | |
| 126960.bj1 | 126960g4 | \([0, -1, 0, -1142733280, -14868059525600]\) | \(544328872410114151778/14166950625\) | \(4295100682631128320000\) | \([2]\) | \(25952256\) | \(3.6663\) |
Rank
sage: E.rank()
The elliptic curves in class 126960g have rank \(1\).
Complex multiplication
The elliptic curves in class 126960g do not have complex multiplication.Modular form 126960.2.a.g
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.
