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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 276138d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
276138.d1 | 276138d1 | \([1, -1, 0, -438111, 113007501]\) | \(-86175179713/1152576\) | \(-124383884731246656\) | \([]\) | \(6082560\) | \(2.0878\) | \(\Gamma_0(N)\)-optimal |
276138.d2 | 276138d2 | \([1, -1, 0, 1561509, 570120633]\) | \(3901777377407/3560891556\) | \(-384284875654163844036\) | \([]\) | \(18247680\) | \(2.6371\) |
Rank
sage: E.rank()
The elliptic curves in class 276138d have rank \(0\).
Complex multiplication
The elliptic curves in class 276138d do not have complex multiplication.Modular form 276138.2.a.d
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 Cremona 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 Cremona labels.