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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 2254b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2254.d2 | 2254b1 | \([1, -1, 0, -401, -14295]\) | \(-60698457/725788\) | \(-85388232412\) | \([2]\) | \(2304\) | \(0.77939\) | \(\Gamma_0(N)\)-optimal |
2254.d1 | 2254b2 | \([1, -1, 0, -11671, -480873]\) | \(1494447319737/5411854\) | \(636699211246\) | \([2]\) | \(4608\) | \(1.1260\) |
Rank
sage: E.rank()
The elliptic curves in class 2254b have rank \(1\).
Complex multiplication
The elliptic curves in class 2254b do not have complex multiplication.Modular form 2254.2.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.