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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 26775g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 26775.r2 | 26775g1 | \([1, -1, 1, -380, 54622]\) | \(-19683/4165\) | \(-1280932734375\) | \([2]\) | \(27648\) | \(1.0025\) | \(\Gamma_0(N)\)-optimal |
| 26775.r1 | 26775g2 | \([1, -1, 1, -24005, 1424872]\) | \(4973940243/50575\) | \(15554183203125\) | \([2]\) | \(55296\) | \(1.3491\) |
Rank
sage: E.rank()
The elliptic curves in class 26775g have rank \(1\).
Complex multiplication
The elliptic curves in class 26775g do not have complex multiplication.Modular form 26775.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
