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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 23184.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
23184.e1 | 23184bb1 | \([0, 0, 0, -178659, -29066014]\) | \(-5702623460245179/252448\) | \(-27918729216\) | \([]\) | \(126720\) | \(1.4865\) | \(\Gamma_0(N)\)-optimal |
23184.e2 | 23184bb2 | \([0, 0, 0, -163539, -34187886]\) | \(-5999796014211/2790817792\) | \(-225000106393337856\) | \([]\) | \(380160\) | \(2.0358\) |
Rank
sage: E.rank()
The elliptic curves in class 23184.e have rank \(1\).
Complex multiplication
The elliptic curves in class 23184.e do not have complex multiplication.Modular form 23184.2.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 LMFDB 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 LMFDB labels.