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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 311696d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
311696.d2 | 311696d1 | \([0, 1, 0, -124159229, -532492771538]\) | \(5610564864985137152/548176896967\) | \(20681159175406120851152\) | \([2]\) | \(39029760\) | \(3.3174\) | \(\Gamma_0(N)\)-optimal |
311696.d1 | 311696d2 | \([0, 1, 0, -1986501084, -34079229074024]\) | \(1436203562785124669552/13712209\) | \(8277163916815211264\) | \([2]\) | \(78059520\) | \(3.6640\) |
Rank
sage: E.rank()
The elliptic curves in class 311696d have rank \(0\).
Complex multiplication
The elliptic curves in class 311696d do not have complex multiplication.Modular form 311696.2.a.d
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.