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SageMath
E = EllipticCurve("di1")
E.isogeny_class()
Elliptic curves in class 106560.di
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 106560.di1 | 106560ce4 | \([0, 0, 0, -184584108, 198718795568]\) | \(3639478711331685826729/2016912141902025000\) | \(385437912648011277926400000\) | \([2]\) | \(35389440\) | \(3.7918\) | |
| 106560.di2 | 106560ce2 | \([0, 0, 0, -112584108, -457086004432]\) | \(825824067562227826729/5613755625000000\) | \(1072805406474240000000000\) | \([2, 2]\) | \(17694720\) | \(3.4452\) | |
| 106560.di3 | 106560ce1 | \([0, 0, 0, -112399788, -458665774288]\) | \(821774646379511057449/38361600000\) | \(7331015924121600000\) | \([2]\) | \(8847360\) | \(3.0987\) | \(\Gamma_0(N)\)-optimal |
| 106560.di4 | 106560ce3 | \([0, 0, 0, -43533228, -1011785533648]\) | \(-47744008200656797609/2286529541015625000\) | \(-436962600000000000000000000\) | \([2]\) | \(35389440\) | \(3.7918\) |
Rank
sage: E.rank()
The elliptic curves in class 106560.di have rank \(1\).
Complex multiplication
The elliptic curves in class 106560.di do not have complex multiplication.Modular form 106560.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
