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SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 147030.bz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
147030.bz1 | 147030j1 | \([1, 0, 0, -140696, 17269056]\) | \(63812982460681/10201800960\) | \(49242144689936640\) | \([2]\) | \(1290240\) | \(1.9254\) | \(\Gamma_0(N)\)-optimal |
147030.bz2 | 147030j2 | \([1, 0, 0, 251384, 96390800]\) | \(363979050334199/1041836936400\) | \(-5028747901147947600\) | \([2]\) | \(2580480\) | \(2.2719\) |
Rank
sage: E.rank()
The elliptic curves in class 147030.bz have rank \(1\).
Complex multiplication
The elliptic curves in class 147030.bz do not have complex multiplication.Modular form 147030.2.a.bz
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.