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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 230384.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
230384.l1 | 230384l2 | \([0, 1, 0, -2362792208, -43082272837100]\) | \(201040818306017728515625/5846438805256620032\) | \(42423594910839697573928763392\) | \([2]\) | \(182476800\) | \(4.2708\) | |
230384.l2 | 230384l1 | \([0, 1, 0, 35989232, -2236781989356]\) | \(710436683544572375/298276259387932672\) | \(-2164386153912505927028703232\) | \([2]\) | \(91238400\) | \(3.9243\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 230384.l have rank \(0\).
Complex multiplication
The elliptic curves in class 230384.l do not have complex multiplication.Modular form 230384.2.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 LMFDB 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 LMFDB labels.