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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 15246.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
15246.l1 | 15246a2 | \([1, -1, 0, -28289157, 57920795477]\) | \(-4904170882875/43904\) | \(-22414147923016789632\) | \([]\) | \(931392\) | \(2.8786\) | |
15246.l2 | 15246a1 | \([1, -1, 0, -178437, 157013973]\) | \(-897199875/14680064\) | \(-10280602434722070528\) | \([]\) | \(310464\) | \(2.3293\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 15246.l have rank \(0\).
Complex multiplication
The elliptic curves in class 15246.l do not have complex multiplication.Modular form 15246.2.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 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.