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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 24400.r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 24400.r1 | 24400b2 | \([0, 0, 0, -30915175, -66064538250]\) | \(816918720558569514576/1385382080078125\) | \(5541528320312500000000\) | \([2]\) | \(1419264\) | \(3.0671\) | |
| 24400.r2 | 24400b1 | \([0, 0, 0, -2542550, -325166125]\) | \(7270967611425540096/4025029246953125\) | \(1006257311738281250000\) | \([2]\) | \(709632\) | \(2.7205\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 24400.r have rank \(1\).
Complex multiplication
The elliptic curves in class 24400.r do not have complex multiplication.Modular form 24400.2.a.r
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
