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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 224400.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
224400.p1 | 224400ek2 | \([0, -1, 0, -135508, 16012012]\) | \(68795769401296/12278839815\) | \(49115359260000000\) | \([2]\) | \(2027520\) | \(1.9220\) | |
224400.p2 | 224400ek1 | \([0, -1, 0, 16367, 1432012]\) | \(1939386712064/4692919275\) | \(-1173229818750000\) | \([2]\) | \(1013760\) | \(1.5755\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 224400.p have rank \(0\).
Complex multiplication
The elliptic curves in class 224400.p do not have complex multiplication.Modular form 224400.2.a.p
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.