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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 3150.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3150.l1 | 3150j2 | \([1, -1, 0, -162, -754]\) | \(139798359/98\) | \(330750\) | \([2]\) | \(768\) | \(-0.0045635\) | |
3150.l2 | 3150j1 | \([1, -1, 0, -12, -4]\) | \(59319/28\) | \(94500\) | \([2]\) | \(384\) | \(-0.35114\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3150.l have rank \(1\).
Complex multiplication
The elliptic curves in class 3150.l do not have complex multiplication.Modular form 3150.2.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.