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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 69300l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
69300.ca1 | 69300l1 | \([0, 0, 0, -7732800, -8276623875]\) | \(10392086293512192/1684375\) | \(8288388281250000\) | \([2]\) | \(1797120\) | \(2.4564\) | \(\Gamma_0(N)\)-optimal |
69300.ca2 | 69300l2 | \([0, 0, 0, -7709175, -8329709250]\) | \(-643570518871152/8271484375\) | \(-651230507812500000000\) | \([2]\) | \(3594240\) | \(2.8030\) |
Rank
sage: E.rank()
The elliptic curves in class 69300l have rank \(0\).
Complex multiplication
The elliptic curves in class 69300l do not have complex multiplication.Modular form 69300.2.a.l
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.