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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 12024.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 12024.c1 | 12024d2 | \([0, 0, 0, -46155, 3815062]\) | \(14566408766500/6777027\) | \(5059023547392\) | \([2]\) | \(28160\) | \(1.3939\) | |
| 12024.c2 | 12024d1 | \([0, 0, 0, -2415, 79666]\) | \(-8346562000/9861183\) | \(-1840333416192\) | \([2]\) | \(14080\) | \(1.0474\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 12024.c have rank \(0\).
Complex multiplication
The elliptic curves in class 12024.c do not have complex multiplication.Modular form 12024.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
