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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 2576e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2576.d2 | 2576e1 | \([0, 1, 0, -28, -84]\) | \(-9826000/3703\) | \(-947968\) | \([2]\) | \(320\) | \(-0.14333\) | \(\Gamma_0(N)\)-optimal |
| 2576.d1 | 2576e2 | \([0, 1, 0, -488, -4316]\) | \(12576878500/1127\) | \(1154048\) | \([2]\) | \(640\) | \(0.20324\) |
Rank
sage: E.rank()
The elliptic curves in class 2576e have rank \(0\).
Complex multiplication
The elliptic curves in class 2576e do not have complex multiplication.Modular form 2576.2.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 Cremona 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 Cremona labels.
