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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 23120.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
23120.z1 | 23120q1 | \([0, 1, 0, -11656, -2034956]\) | \(-1771561/17000\) | \(-1680747204608000\) | \([]\) | \(82944\) | \(1.6039\) | \(\Gamma_0(N)\)-optimal |
23120.z2 | 23120q2 | \([0, 1, 0, 103944, 52112084]\) | \(1256216039/12577280\) | \(-1243484011857182720\) | \([]\) | \(248832\) | \(2.1532\) |
Rank
sage: E.rank()
The elliptic curves in class 23120.z have rank \(0\).
Complex multiplication
The elliptic curves in class 23120.z do not have complex multiplication.Modular form 23120.2.a.z
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.