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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 301530.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
301530.l1 | 301530l2 | \([1, 1, 0, -856197, -305289891]\) | \(468898230633769/5540400\) | \(820178039415600\) | \([2]\) | \(4730880\) | \(2.0117\) | |
301530.l2 | 301530l1 | \([1, 1, 0, -52117, -5046419]\) | \(-105756712489/12476160\) | \(-1846919436906240\) | \([2]\) | \(2365440\) | \(1.6652\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 301530.l have rank \(0\).
Complex multiplication
The elliptic curves in class 301530.l do not have complex multiplication.Modular form 301530.2.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.