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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 21780u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 21780.t2 | 21780u1 | \([0, 0, 0, 3993, 673486]\) | \(176/5\) | \(-200022559038720\) | \([]\) | \(47520\) | \(1.4242\) | \(\Gamma_0(N)\)-optimal |
| 21780.t1 | 21780u2 | \([0, 0, 0, -475167, 126117574]\) | \(-296587984/125\) | \(-5000563975968000\) | \([3]\) | \(142560\) | \(1.9735\) |
Rank
sage: E.rank()
The elliptic curves in class 21780u have rank \(1\).
Complex multiplication
The elliptic curves in class 21780u do not have complex multiplication.Modular form 21780.2.a.u
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
