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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 93600.bv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
93600.bv1 | 93600cv2 | \([0, 0, 0, -8700, -284000]\) | \(42144192/4225\) | \(7300800000000\) | \([2]\) | \(147456\) | \(1.2045\) | |
93600.bv2 | 93600cv1 | \([0, 0, 0, 675, -21500]\) | \(1259712/8125\) | \(-219375000000\) | \([2]\) | \(73728\) | \(0.85795\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 93600.bv have rank \(1\).
Complex multiplication
The elliptic curves in class 93600.bv do not have complex multiplication.Modular form 93600.2.a.bv
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.