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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 54150.bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
54150.bc1 | 54150v1 | \([1, 0, 1, -901, -12052]\) | \(-14317849/2700\) | \(-15229687500\) | \([]\) | \(62208\) | \(0.67799\) | \(\Gamma_0(N)\)-optimal |
54150.bc2 | 54150v2 | \([1, 0, 1, 6224, 59198]\) | \(4728305591/3000000\) | \(-16921875000000\) | \([]\) | \(186624\) | \(1.2273\) |
Rank
sage: E.rank()
The elliptic curves in class 54150.bc have rank \(1\).
Complex multiplication
The elliptic curves in class 54150.bc do not have complex multiplication.Modular form 54150.2.a.bc
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.