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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 104742e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
104742.q2 | 104742e1 | \([1, -1, 0, 17358, -1308870]\) | \(144703125/267674\) | \(-1069884680909022\) | \([]\) | \(456192\) | \(1.5686\) | \(\Gamma_0(N)\)-optimal |
104742.q1 | 104742e2 | \([1, -1, 0, -165147, 48198653]\) | \(-170953875/244904\) | \(-713598924902109048\) | \([]\) | \(1368576\) | \(2.1179\) |
Rank
sage: E.rank()
The elliptic curves in class 104742e have rank \(1\).
Complex multiplication
The elliptic curves in class 104742e do not have complex multiplication.Modular form 104742.2.a.e
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.