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SageMath
E = EllipticCurve("eb1")
E.isogeny_class()
Elliptic curves in class 466752.eb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
466752.eb1 | 466752eb4 | \([0, 1, 0, -160617801217, -24776466871606177]\) | \(1748094148784980747354970849498497/887694600425282263291392\) | \(232703813333885193628258664448\) | \([2]\) | \(1815478272\) | \(4.9677\) | |
466752.eb2 | 466752eb3 | \([0, 1, 0, -21971478017, 689374449575007]\) | \(4474676144192042711273397261697/1806328356954994499451382272\) | \(473518140805610078064183154311168\) | \([2]\) | \(1815478272\) | \(4.9677\) | \(\Gamma_0(N)\)-optimal* |
466752.eb3 | 466752eb2 | \([0, 1, 0, -10092914177, -382734832655265]\) | \(433744050935826360922067531137/9612122270219882316693504\) | \(2519760180404520830027301912576\) | \([2, 2]\) | \(907739136\) | \(4.6211\) | \(\Gamma_0(N)\)-optimal* |
466752.eb4 | 466752eb1 | \([0, 1, 0, 57301503, -18331939527585]\) | \(79374649975090937760383/553856914190911653543936\) | \(-145190266913662344506621558784\) | \([2]\) | \(453869568\) | \(4.2746\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 466752.eb have rank \(0\).
Complex multiplication
The elliptic curves in class 466752.eb do not have complex multiplication.Modular form 466752.2.a.eb
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.