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SageMath
E = EllipticCurve("iv1")
E.isogeny_class()
Elliptic curves in class 235950.iv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
235950.iv1 | 235950iv2 | \([1, 0, 0, -10173138, 12490181892]\) | \(-168256703745625/30371328\) | \(-21017445391800000000\) | \([]\) | \(13996800\) | \(2.7114\) | |
235950.iv2 | 235950iv1 | \([1, 0, 0, 36237, 57205017]\) | \(7604375/2047032\) | \(-1416578928496875000\) | \([]\) | \(4665600\) | \(2.1621\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 235950.iv have rank \(1\).
Complex multiplication
The elliptic curves in class 235950.iv do not have complex multiplication.Modular form 235950.2.a.iv
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.