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SageMath
E = EllipticCurve("eb1")
E.isogeny_class()
Elliptic curves in class 254898.eb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 254898.eb1 | 254898eb2 | \([1, -1, 1, -16379852, -4842580305]\) | \(234770924809/130960928\) | \(271113435624235952899872\) | \([2]\) | \(53084160\) | \(3.1867\) | |
| 254898.eb2 | 254898eb1 | \([1, -1, 1, 4011988, -601077585]\) | \(3449795831/2071552\) | \(-4288497251594439195648\) | \([2]\) | \(26542080\) | \(2.8401\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 254898.eb have rank \(0\).
Complex multiplication
The elliptic curves in class 254898.eb do not have complex multiplication.Modular form 254898.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
