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SageMath
E = EllipticCurve("dc1")
E.isogeny_class()
Elliptic curves in class 38025.dc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 38025.dc1 | 38025cp1 | \([0, 0, 1, -12675, 562981]\) | \(-102400/3\) | \(-6597644551875\) | \([]\) | \(112320\) | \(1.2387\) | \(\Gamma_0(N)\)-optimal |
| 38025.dc2 | 38025cp2 | \([0, 0, 1, 63375, -27119219]\) | \(20480/243\) | \(-334005755438671875\) | \([]\) | \(561600\) | \(2.0434\) |
Rank
sage: E.rank()
The elliptic curves in class 38025.dc have rank \(1\).
Complex multiplication
The elliptic curves in class 38025.dc do not have complex multiplication.Modular form 38025.2.a.dc
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
