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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 107800r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 107800.n2 | 107800r1 | \([0, 1, 0, 53492, 643488]\) | \(35969456/21175\) | \(-9964870300000000\) | \([2]\) | \(589824\) | \(1.7592\) | \(\Gamma_0(N)\)-optimal |
| 107800.n1 | 107800r2 | \([0, 1, 0, -216008, 4955488]\) | \(592143556/336875\) | \(634128110000000000\) | \([2]\) | \(1179648\) | \(2.1058\) |
Rank
sage: E.rank()
The elliptic curves in class 107800r have rank \(1\).
Complex multiplication
The elliptic curves in class 107800r do not have complex multiplication.Modular form 107800.2.a.r
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.
