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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 343850.bv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
343850.bv1 | 343850bv2 | \([1, 1, 0, -5993845, 5645655405]\) | \(-6434774386429585/140608\) | \(-520375757012800\) | \([]\) | \(12830400\) | \(2.3501\) | |
343850.bv2 | 343850bv1 | \([1, 1, 0, -69045, 8800685]\) | \(-9836106385/3407872\) | \(-12612184027955200\) | \([]\) | \(4276800\) | \(1.8008\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 343850.bv have rank \(0\).
Complex multiplication
The elliptic curves in class 343850.bv do not have complex multiplication.Modular form 343850.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.