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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 26775.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 26775.m1 | 26775w4 | \([1, -1, 1, -13770230, 19671428522]\) | \(25351269426118370449/27551475\) | \(313828519921875\) | \([2]\) | \(589824\) | \(2.5004\) | |
| 26775.m2 | 26775w3 | \([1, -1, 1, -1073480, 144070022]\) | \(12010404962647729/6166198828125\) | \(70236858526611328125\) | \([2]\) | \(589824\) | \(2.5004\) | |
| 26775.m3 | 26775w2 | \([1, -1, 1, -860855, 307366022]\) | \(6193921595708449/6452105625\) | \(73493515634765625\) | \([2, 2]\) | \(294912\) | \(2.1538\) | |
| 26775.m4 | 26775w1 | \([1, -1, 1, -40730, 7200272]\) | \(-656008386769/1581036975\) | \(-18008999293359375\) | \([2]\) | \(147456\) | \(1.8073\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 26775.m have rank \(0\).
Complex multiplication
The elliptic curves in class 26775.m do not have complex multiplication.Modular form 26775.2.a.m
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
