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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 13860.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
13860.b1 | 13860i2 | \([0, 0, 0, -4863, 9718]\) | \(68150496976/39220335\) | \(7319455799040\) | \([2]\) | \(27648\) | \(1.1581\) | |
13860.b2 | 13860i1 | \([0, 0, 0, 1212, 1213]\) | \(16880451584/9823275\) | \(-114578679600\) | \([2]\) | \(13824\) | \(0.81148\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 13860.b have rank \(1\).
Complex multiplication
The elliptic curves in class 13860.b do not have complex multiplication.Modular form 13860.2.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 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.