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SageMath
E = EllipticCurve("dc1")
E.isogeny_class()
Elliptic curves in class 258570.dc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
258570.dc1 | 258570dc1 | \([1, -1, 1, -26903, -755153]\) | \(611960049/282880\) | \(995382235111680\) | \([2]\) | \(1376256\) | \(1.5725\) | \(\Gamma_0(N)\)-optimal |
258570.dc2 | 258570dc2 | \([1, -1, 1, 94777, -5768369]\) | \(26757728271/19536400\) | \(-68743585612400400\) | \([2]\) | \(2752512\) | \(1.9191\) |
Rank
sage: E.rank()
The elliptic curves in class 258570.dc have rank \(1\).
Complex multiplication
The elliptic curves in class 258570.dc do not have complex multiplication.Modular form 258570.2.a.dc
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.