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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 30015.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
30015.d1 | 30015m1 | \([1, -1, 1, -3362, -74176]\) | \(5763259856089/450225\) | \(328214025\) | \([2]\) | \(13824\) | \(0.68134\) | \(\Gamma_0(N)\)-optimal |
30015.d2 | 30015m2 | \([1, -1, 1, -3137, -84706]\) | \(-4681768588489/1621620405\) | \(-1182161275245\) | \([2]\) | \(27648\) | \(1.0279\) |
Rank
sage: E.rank()
The elliptic curves in class 30015.d have rank \(0\).
Complex multiplication
The elliptic curves in class 30015.d do not have complex multiplication.Modular form 30015.2.a.d
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.