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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 91035.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 91035.x1 | 91035bt2 | \([1, -1, 1, -10605632, 13296550646]\) | \(1526038582697/2205\) | \(190623489135720165\) | \([2]\) | \(2228224\) | \(2.5864\) | |
| 91035.x2 | 91035bt1 | \([1, -1, 1, -656807, 211856006]\) | \(-362467097/14175\) | \(-1225436715872486775\) | \([2]\) | \(1114112\) | \(2.2398\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 91035.x have rank \(0\).
Complex multiplication
The elliptic curves in class 91035.x do not have complex multiplication.Modular form 91035.2.a.x
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
