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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 90972c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
90972.h2 | 90972c1 | \([0, 0, 0, -1005024, -392039863]\) | \(-204589760512/2600283\) | \(-1426887499871543472\) | \([2]\) | \(1105920\) | \(2.2931\) | \(\Gamma_0(N)\)-optimal |
90972.h1 | 90972c2 | \([0, 0, 0, -16129119, -24932396410]\) | \(52852623679312/8379\) | \(73566702463838976\) | \([2]\) | \(2211840\) | \(2.6397\) |
Rank
sage: E.rank()
The elliptic curves in class 90972c have rank \(0\).
Complex multiplication
The elliptic curves in class 90972c do not have complex multiplication.Modular form 90972.2.a.c
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.