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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 23120.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
23120.e1 | 23120s1 | \([0, 1, 0, -34776, -2173676]\) | \(47045881/6800\) | \(672298881843200\) | \([2]\) | \(110592\) | \(1.5705\) | \(\Gamma_0(N)\)-optimal |
23120.e2 | 23120s2 | \([0, 1, 0, 57704, -11680620]\) | \(214921799/722500\) | \(-71431756195840000\) | \([2]\) | \(221184\) | \(1.9170\) |
Rank
sage: E.rank()
The elliptic curves in class 23120.e have rank \(2\).
Complex multiplication
The elliptic curves in class 23120.e do not have complex multiplication.Modular form 23120.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.