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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 3150u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3150.m2 | 3150u1 | \([1, -1, 0, 1008, -10584]\) | \(397535/392\) | \(-111628125000\) | \([]\) | \(3600\) | \(0.80685\) | \(\Gamma_0(N)\)-optimal |
3150.m1 | 3150u2 | \([1, -1, 0, -10242, 563166]\) | \(-417267265/235298\) | \(-67004782031250\) | \([3]\) | \(10800\) | \(1.3562\) |
Rank
sage: E.rank()
The elliptic curves in class 3150u have rank \(0\).
Complex multiplication
The elliptic curves in class 3150u do not have complex multiplication.Modular form 3150.2.a.u
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 Cremona 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 Cremona labels.