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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 19404.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 19404.c1 | 19404w1 | \([0, 0, 0, -7603869, 8156685089]\) | \(-35431687725461248/440311012911\) | \(-604220281775318211696\) | \([]\) | \(1244160\) | \(2.7980\) | \(\Gamma_0(N)\)-optimal |
| 19404.c2 | 19404w2 | \([0, 0, 0, 26450151, 41683653641]\) | \(1491325446082364672/1410025768453071\) | \(-1934919050724225123321456\) | \([]\) | \(3732480\) | \(3.3473\) |
Rank
sage: E.rank()
The elliptic curves in class 19404.c have rank \(0\).
Complex multiplication
The elliptic curves in class 19404.c do not have complex multiplication.Modular form 19404.2.a.c
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.
