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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 21294d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
21294.t2 | 21294d1 | \([1, -1, 0, 13789608, -2865988800]\) | \(77908020328125/46036680704\) | \(-171356779032859788705792\) | \([]\) | \(3032640\) | \(3.1475\) | \(\Gamma_0(N)\)-optimal |
21294.t1 | 21294d2 | \([1, -1, 0, -205558872, -1190140818112]\) | \(-354003515818875/20661046784\) | \(-56063103655633985954953728\) | \([]\) | \(9097920\) | \(3.6968\) |
Rank
sage: E.rank()
The elliptic curves in class 21294d have rank \(1\).
Complex multiplication
The elliptic curves in class 21294d do not have complex multiplication.Modular form 21294.2.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.