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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 118354d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
118354.j2 | 118354d1 | \([1, 1, 0, -107350631, -425839505611]\) | \(3243586268529106417/20244571000832\) | \(853926808148207214989312\) | \([2]\) | \(25056000\) | \(3.4298\) | \(\Gamma_0(N)\)-optimal |
118354.j1 | 118354d2 | \([1, 1, 0, -173071911, 157252834805]\) | \(13592251860742707697/7612392968095424\) | \(321094797679260871730158784\) | \([2]\) | \(50112000\) | \(3.7764\) |
Rank
sage: E.rank()
The elliptic curves in class 118354d have rank \(0\).
Complex multiplication
The elliptic curves in class 118354d do not have complex multiplication.Modular form 118354.2.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.