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SageMath
E = EllipticCurve("di1")
E.isogeny_class()
Elliptic curves in class 296450.di
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
296450.di1 | 296450di1 | \([1, -1, 0, -2310457, -1350831399]\) | \(52355598021/15092\) | \(393188820037898500\) | \([2]\) | \(6635520\) | \(2.3561\) | \(\Gamma_0(N)\)-optimal |
296450.di2 | 296450di2 | \([1, -1, 0, -2014007, -1710425249]\) | \(-34677868581/28471058\) | \(-741750709001495520250\) | \([2]\) | \(13271040\) | \(2.7027\) |
Rank
sage: E.rank()
The elliptic curves in class 296450.di have rank \(0\).
Complex multiplication
The elliptic curves in class 296450.di do not have complex multiplication.Modular form 296450.2.a.di
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.