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SageMath
E = EllipticCurve("di1")
E.isogeny_class()
Elliptic curves in class 350658.di
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 350658.di1 | 350658di2 | \([1, -1, 1, -144414590, -667945834531]\) | \(3776104682692733708238625/3408048\) | \(300620506032\) | \([]\) | \(19906560\) | \(2.8825\) | |
| 350658.di2 | 350658di1 | \([1, -1, 1, -1783310, -915406819]\) | \(7110352307247726625/6866458324992\) | \(605683422389219328\) | \([]\) | \(6635520\) | \(2.3332\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 350658.di have rank \(0\).
Complex multiplication
The elliptic curves in class 350658.di do not have complex multiplication.Modular form 350658.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
