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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 394944.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
394944.q1 | 394944q2 | \([0, -1, 0, -23112129, -42650072991]\) | \(2940001530995593/8673562656\) | \(4028037944423485538304\) | \([2]\) | \(22118400\) | \(3.0156\) | |
394944.q2 | 394944q1 | \([0, -1, 0, -2048449, -55099295]\) | \(2046931732873/1181672448\) | \(548773514091253727232\) | \([2]\) | \(11059200\) | \(2.6690\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 394944.q have rank \(0\).
Complex multiplication
The elliptic curves in class 394944.q do not have complex multiplication.Modular form 394944.2.a.q
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.