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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 912.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
912.l1 | 912d1 | \([0, 1, 0, -16, -28]\) | \(470596/57\) | \(58368\) | \([2]\) | \(160\) | \(-0.35492\) | \(\Gamma_0(N)\)-optimal |
912.l2 | 912d2 | \([0, 1, 0, 24, -108]\) | \(715822/3249\) | \(-6653952\) | \([2]\) | \(320\) | \(-0.0083494\) |
Rank
sage: E.rank()
The elliptic curves in class 912.l have rank \(0\).
Complex multiplication
The elliptic curves in class 912.l do not have complex multiplication.Modular form 912.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.