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SageMath
E = EllipticCurve("cr1")
E.isogeny_class()
Elliptic curves in class 30576cr
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 30576.bw3 | 30576cr1 | \([0, 1, 0, 10568, 3979604]\) | \(270840023/14329224\) | \(-6905114109444096\) | \([]\) | \(248832\) | \(1.7189\) | \(\Gamma_0(N)\)-optimal |
| 30576.bw2 | 30576cr2 | \([0, 1, 0, -95272, -108422476]\) | \(-198461344537/10417365504\) | \(-5020027429601673216\) | \([]\) | \(746496\) | \(2.2683\) | |
| 30576.bw1 | 30576cr3 | \([0, 1, 0, -20428312, -35545700716]\) | \(-1956469094246217097/36641439744\) | \(-17657154537233842176\) | \([]\) | \(2239488\) | \(2.8176\) |
Rank
sage: E.rank()
The elliptic curves in class 30576cr have rank \(2\).
Complex multiplication
The elliptic curves in class 30576cr do not have complex multiplication.Modular form 30576.2.a.cr
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
