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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 3150.bg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3150.bg1 | 3150br2 | \([1, -1, 1, -3155, 72947]\) | \(-7620530425/526848\) | \(-240045120000\) | \([3]\) | \(5184\) | \(0.93462\) | |
3150.bg2 | 3150br1 | \([1, -1, 1, 220, 47]\) | \(2595575/1512\) | \(-688905000\) | \([]\) | \(1728\) | \(0.38532\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3150.bg have rank \(1\).
Complex multiplication
The elliptic curves in class 3150.bg do not have complex multiplication.Modular form 3150.2.a.bg
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.