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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 251826b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
251826.b1 | 251826b1 | \([1, 1, 0, -211005, 37212777]\) | \(96386901625/18468\) | \(199070548695972\) | \([2]\) | \(2027680\) | \(1.7444\) | \(\Gamma_0(N)\)-optimal |
251826.b2 | 251826b2 | \([1, 1, 0, -188915, 45337479]\) | \(-69173457625/42633378\) | \(-459554361664651362\) | \([2]\) | \(4055360\) | \(2.0910\) |
Rank
sage: E.rank()
The elliptic curves in class 251826b have rank \(0\).
Complex multiplication
The elliptic curves in class 251826b do not have complex multiplication.Modular form 251826.2.a.b
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.