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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 2448l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2448.a2 | 2448l1 | \([0, 0, 0, -24, 284]\) | \(-221184/4913\) | \(-33958656\) | \([]\) | \(576\) | \(0.12585\) | \(\Gamma_0(N)\)-optimal |
2448.a1 | 2448l2 | \([0, 0, 0, -4104, 101196]\) | \(-1517101056/17\) | \(-85660416\) | \([]\) | \(1728\) | \(0.67515\) |
Rank
sage: E.rank()
The elliptic curves in class 2448l have rank \(1\).
Complex multiplication
The elliptic curves in class 2448l do not have complex multiplication.Modular form 2448.2.a.l
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.