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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 348075.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 348075.w1 | 348075w1 | \([1, -1, 1, -1170230, 487482772]\) | \(420100556152674123/62939003491\) | \(26552392097765625\) | \([2]\) | \(3686400\) | \(2.1648\) | \(\Gamma_0(N)\)-optimal |
| 348075.w2 | 348075w2 | \([1, -1, 1, -1061855, 581335522]\) | \(-313859434290315003/164114213839849\) | \(-69235683963686296875\) | \([2]\) | \(7372800\) | \(2.5113\) |
Rank
sage: E.rank()
The elliptic curves in class 348075.w have rank \(2\).
Complex multiplication
The elliptic curves in class 348075.w do not have complex multiplication.Modular form 348075.2.a.w
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.
