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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 286121e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
286121.e1 | 286121e1 | \([0, 1, 1, -37419, 3245734]\) | \(-2258403328/480491\) | \(-1232808447986819\) | \([]\) | \(1205280\) | \(1.6170\) | \(\Gamma_0(N)\)-optimal |
286121.e2 | 286121e2 | \([0, 1, 1, 263761, -18755465]\) | \(790939860992/517504691\) | \(-1327775452480084619\) | \([]\) | \(3615840\) | \(2.1663\) |
Rank
sage: E.rank()
The elliptic curves in class 286121e have rank \(0\).
Complex multiplication
The elliptic curves in class 286121e do not have complex multiplication.Modular form 286121.2.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.