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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 311696bl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
311696.bl2 | 311696bl1 | \([0, 0, 0, -15851, 3575066]\) | \(-60698457/725788\) | \(-5266545520918528\) | \([2]\) | \(1474560\) | \(1.6985\) | \(\Gamma_0(N)\)-optimal |
311696.bl1 | 311696bl2 | \([0, 0, 0, -461131, 120149370]\) | \(1494447319737/5411854\) | \(39270111166849024\) | \([2]\) | \(2949120\) | \(2.0451\) |
Rank
sage: E.rank()
The elliptic curves in class 311696bl have rank \(2\).
Complex multiplication
The elliptic curves in class 311696bl do not have complex multiplication.Modular form 311696.2.a.bl
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.