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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 215475u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
215475.m2 | 215475u1 | \([1, 1, 1, -139513, -19075594]\) | \(3981876625/232713\) | \(17550956294015625\) | \([2]\) | \(1548288\) | \(1.8705\) | \(\Gamma_0(N)\)-optimal |
215475.m1 | 215475u2 | \([1, 1, 1, -414138, 78690906]\) | \(104154702625/24649677\) | \(1859051293604578125\) | \([2]\) | \(3096576\) | \(2.2171\) |
Rank
sage: E.rank()
The elliptic curves in class 215475u have rank \(1\).
Complex multiplication
The elliptic curves in class 215475u do not have complex multiplication.Modular form 215475.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.