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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 5445i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5445.j1 | 5445i1 | \([1, -1, 0, -14724, -414045]\) | \(205379/75\) | \(128920790005425\) | \([2]\) | \(16896\) | \(1.4079\) | \(\Gamma_0(N)\)-optimal |
5445.j2 | 5445i2 | \([1, -1, 0, 45171, -2965572]\) | \(5929741/5625\) | \(-9669059250406875\) | \([2]\) | \(33792\) | \(1.7545\) |
Rank
sage: E.rank()
The elliptic curves in class 5445i have rank \(1\).
Complex multiplication
The elliptic curves in class 5445i do not have complex multiplication.Modular form 5445.2.a.i
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.