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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 2025.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2025.d1 | 2025a2 | \([0, 0, 1, -4050, -98719]\) | \(884736/5\) | \(41518828125\) | \([]\) | \(1728\) | \(0.87939\) | |
| 2025.d2 | 2025a1 | \([0, 0, 1, -300, 1906]\) | \(2359296/125\) | \(158203125\) | \([]\) | \(576\) | \(0.33008\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2025.d have rank \(1\).
Complex multiplication
The elliptic curves in class 2025.d do not have complex multiplication.Modular form 2025.2.a.d
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.
