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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 26688.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 26688.m1 | 26688f1 | \([0, -1, 0, -4993, 137473]\) | \(210094874500/3753\) | \(245956608\) | \([2]\) | \(21504\) | \(0.73709\) | \(\Gamma_0(N)\)-optimal |
| 26688.m2 | 26688f2 | \([0, -1, 0, -4833, 146529]\) | \(-95269531250/14085009\) | \(-1846150299648\) | \([2]\) | \(43008\) | \(1.0837\) |
Rank
sage: E.rank()
The elliptic curves in class 26688.m have rank \(0\).
Complex multiplication
The elliptic curves in class 26688.m do not have complex multiplication.Modular form 26688.2.a.m
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.
