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SageMath
E = EllipticCurve("cd1")
E.isogeny_class()
Elliptic curves in class 275880.cd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 275880.cd1 | 275880cd3 | \([0, 1, 0, -3973680, 3047534928]\) | \(3825131988299044/961875\) | \(1744916722560000\) | \([2]\) | \(6553600\) | \(2.2998\) | |
| 275880.cd2 | 275880cd2 | \([0, 1, 0, -249300, 47174400]\) | \(3778298043856/59213025\) | \(26854268360198400\) | \([2, 2]\) | \(3276800\) | \(1.9532\) | |
| 275880.cd3 | 275880cd1 | \([0, 1, 0, -30895, -962062]\) | \(115060504576/52780005\) | \(1496047975004880\) | \([2]\) | \(1638400\) | \(1.6066\) | \(\Gamma_0(N)\)-optimal |
| 275880.cd4 | 275880cd4 | \([0, 1, 0, -19400, 131041920]\) | \(-445138564/4089438495\) | \(-7418562303632071680\) | \([2]\) | \(6553600\) | \(2.2998\) |
Rank
sage: E.rank()
The elliptic curves in class 275880.cd have rank \(1\).
Complex multiplication
The elliptic curves in class 275880.cd do not have complex multiplication.Modular form 275880.2.a.cd
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
