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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 9282l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9282.i1 | 9282l1 | \([1, 0, 1, -13044382, 18132484496]\) | \(245467607504992533120574297/1733763438231552\) | \(1733763438231552\) | \([2]\) | \(349440\) | \(2.5220\) | \(\Gamma_0(N)\)-optimal |
9282.i2 | 9282l2 | \([1, 0, 1, -13036062, 18156772240]\) | \(-244998212735457942818233177/652408656229361356416\) | \(-652408656229361356416\) | \([2]\) | \(698880\) | \(2.8686\) |
Rank
sage: E.rank()
The elliptic curves in class 9282l have rank \(0\).
Complex multiplication
The elliptic curves in class 9282l do not have complex multiplication.Modular form 9282.2.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.