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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 141610bd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
141610.cv2 | 141610bd1 | \([1, 1, 1, -295, -73403]\) | \(-49/40\) | \(-2318172126760\) | \([]\) | \(276480\) | \(1.0517\) | \(\Gamma_0(N)\)-optimal |
141610.cv1 | 141610bd2 | \([1, 1, 1, -141905, -20635175]\) | \(-5452947409/250\) | \(-14488575792250\) | \([]\) | \(829440\) | \(1.6010\) |
Rank
sage: E.rank()
The elliptic curves in class 141610bd have rank \(1\).
Complex multiplication
The elliptic curves in class 141610bd do not have complex multiplication.Modular form 141610.2.a.bd
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.