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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 30400br
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 30400.q2 | 30400br1 | \([0, -1, 0, -24833, -1498463]\) | \(-413493625/152\) | \(-622592000000\) | \([]\) | \(55296\) | \(1.2310\) | \(\Gamma_0(N)\)-optimal |
| 30400.q3 | 30400br2 | \([0, -1, 0, 15167, -5730463]\) | \(94196375/3511808\) | \(-14384365568000000\) | \([]\) | \(165888\) | \(1.7803\) | |
| 30400.q1 | 30400br3 | \([0, -1, 0, -136833, 156757537]\) | \(-69173457625/2550136832\) | \(-10445360463872000000\) | \([]\) | \(497664\) | \(2.3296\) |
Rank
sage: E.rank()
The elliptic curves in class 30400br have rank \(1\).
Complex multiplication
The elliptic curves in class 30400br do not have complex multiplication.Modular form 30400.2.a.br
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.
